A022562 -id:A022562 - cp's OEIS frontend

A300913 Number of non-isomorphic connected set-systems of weight n.

1, 1, 1, 2, 4, 7, 18, 37, 96, 239, 658, 1810, 5358, 16057, 50373, 161811, 536964, 1826151, 6380481, 22822280, 83587920, 312954111, 1197178941, 4674642341, 18620255306, 75606404857, 312763294254, 1317356836235, 5646694922172, 24618969819915, 109125629486233, 491554330852608

Offset: 0

Gus Wiseman, Jun 19 2018

nonn

The weight of a set-system is the sum of cardinalities of the sets. Weight is generally not the same as number of vertices.

			Non-isomorphic representatives of the a(1) = 1 through a(5) = 7 set systems:
1: {{1}}
2: {{1,2}}
3: {{1,2,3}}
   {{2},{1,2}}
4: {{1,2,3,4}}
   {{3},{1,2,3}}
   {{1,3},{2,3}}
   {{1},{2},{1,2}}
5: {{1,2,3,4,5}}
   {{4},{1,2,3,4}}
   {{1,4},{2,3,4}}
   {{2,3},{1,2,3}}
   {{2},{3},{1,2,3}}
   {{2},{1,3},{2,3}}
   {{3},{1,3},{2,3}}
Non-isomorphic representatives of the a(6) = 18 connected set-systems:
  {{1,2,3,4,5,6}}
  {{5},{1,2,3,4,5}}
  {{1,5},{2,3,4,5}}
  {{3,4},{1,2,3,4}}
  {{1,2,5},{3,4,5}}
  {{1,3,4},{2,3,4}}
  {{1},{1,4},{2,3,4}}
  {{1},{2,3},{1,2,3}}
  {{3},{4},{1,2,3,4}}
  {{3},{1,4},{2,3,4}}
  {{3},{2,3},{1,2,3}}
  {{4},{1,4},{2,3,4}}
  {{1,2},{1,3},{2,3}}
  {{1,3},{2,4},{3,4}}
  {{1,4},{2,4},{3,4}}
  {{1},{2},{3},{1,2,3}}
  {{1},{2},{1,3},{2,3}}
  {{2},{3},{1,3},{2,3}}

Jean-François Alcover, Table of n, a(n) for n = 0..50 [using Andrew Howroyd's b-file for A283877]

Cf. A007716, A055621, A283877, A293606, A293607.

A283877 = Import["https://oeis.org/A283877/b283877.txt", "Table"][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
{1} ~Join~ EulerInvTransform[A283877 // Rest] (* Jean-François Alcover, Nov 07 2019, updated Mar 17 2020 *)

Inverse Euler transform of A283877.

a(11)-a(31) from Jean-François Alcover, Nov 07 2019

A056156 Number of connected bipartite graphs with n edges, no isolated vertices and a distinguished bipartite block, up to isomorphism.

Original entry on oeis.org

1, 2, 3, 7, 12, 32, 67, 181, 458, 1295, 3642, 10975, 33448, 106424, 345964, 1159489, 3975367, 13977808, 50238606, 184629655, 692757132, 2652892219, 10359676617, 41233344350, 167171988557, 690054189750, 2898637406813, 12385234548345

Offset: 1

Vladeta Jovovic, Jul 30 2000

nonn

EULERi transform of A049311.

Also the number of non-isomorphic connected set multipartitions (multisets of sets) of weight n. The weight of a set multipartition is the sum of sizes of its parts. Weight is generally not the same as number of vertices. - Gus Wiseman, Sep 23 2018

			From _Gus Wiseman_, Sep 24 2018: (Start)
Non-isomorphic representatives of the a(1) = 1 through a(4) = 7 connected set multipartitions:
  {{1}}   {{1,2}}     {{1,2,3}}      {{1,2,3,4}}
         {{1},{1}}   {{2},{1,2}}    {{3},{1,2,3}}
                    {{1},{1},{1}}   {{1,2},{1,2}}
                                    {{1,3},{2,3}}
                                   {{1},{2},{1,2}}
                                   {{2},{2},{1,2}}
                                  {{1},{1},{1},{1}}
(End)

Jean-François Alcover, Table of n, a(n) for n = 1..102
Daniel R. Herber, Enhancements to the perfect matching approach for graph enumeration-based engineering challenges, Proceedings of the ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE 2020).
N. J. A. Sloane, Transforms

Cf. A007716, A007718, A056156, A319557, A319565, A319566.

A049311 = Cases[Import["https://oeis.org/A049311/b049311.txt", "Table"], {, }][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
EulerInvTransform[A049311] (* Jean-François Alcover, Mar 16 2020 *)

More terms from Max Alekseyev, Jul 22 2009

A002905 Number of connected graphs with n edges.

Original entry on oeis.org

1, 1, 1, 3, 5, 12, 30, 79, 227, 710, 2322, 8071, 29503, 112822, 450141, 1867871, 8037472, 35787667, 164551477, 779945969, 3804967442, 19079312775, 98211456209, 518397621443, 2802993986619, 15510781288250, 87765472487659, 507395402140211, 2994893000122118, 18035546081743772, 110741792670074054, 692894304050453139

Offset: 0

N. J. A. Sloane

			a(3) = 3 since the three connected graphs with three edges are a path, a triangle and a "Y".
The first difference between this sequence and A046091 is for n=9 edges where we see K_{3,3}, the well-known "utility graph".

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Max Alekseyev, Table of n, a(n) for n = 0..60
G. A. Baker et al., High-temperature expansions for the spin-1/2 Heisenberg model, Phys. Rev., 164 (1967), 800-817.
Nicolas Borie, The Hopf Algebra of graph invariants, arXiv preprint arXiv:1511.05843 [math.CO], 2015.
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
Mike Cummings and Adam Van Tuyl, The GeometricDecomposability package for Macaulay2, arXiv:2211.02471 [math.AC], 2022.
Anjan Dutta and Hichem Sahbi, Graph Kernels based on High Order Graphlet Parsing and Hashing, arXiv:1803.00425 [cs.CV], 2018.
Gordon Royle, Small graphs
M. L. Stein and P. R. Stein, Enumeration of Linear Graphs and Connected Linear Graphs up to p = 18 Points. Report LA-3775, Los Alamos Scientific Laboratory of the University of California, Los Alamos, NM, Oct 1967
Peter Steinbach, Field Guide to Simple Graphs, Volume 4, Part 1 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)
Eric Weisstein's World of Mathematics, Polynema.

Column sums of A054924 or equivalently row sums of A054923.
Cf. A000664, A046091 (for connected planar graphs), A275421 (multisets).
Apart from a(3), same as A003089.

A000664 = Cases[Import["https://oeis.org/A000664/b000664.txt", "Table"], {, }][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
Join[{1}, EulerInvTransform[Rest @ A000664]] (* Jean-François Alcover, May 10 2019, updated Mar 17 2020 *)

A000664 and this sequence are an Euler transform pair. - N. J. A. Sloane, Aug 30 2016

More terms from Vladeta Jovovic, Jan 12 2000
More terms from Gordon F. Royle, Jun 05 2003
a(25)-a(26) from Max Alekseyev, Sep 19 2009
a(27)-a(60) from Max Alekseyev, Sep 07 2016

A003049 Number of connected Eulerian graphs with n unlabeled nodes.

Original entry on oeis.org

1, 0, 1, 1, 4, 8, 37, 184, 1782, 31026, 1148626, 86539128, 12798435868, 3620169692289, 1940367005824561, 1965937435288738165, 3766548132138130650270, 13666503289976224080346733

Offset: 1

N. J. A. Sloane

These are connected graphs with every node of even degree (cf. A002854).

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 117.
Valery A. Liskovets, Enumeration of Euler graphs. (Russian), Vesci Akad. Navuk BSSR, Ser. Fiz.-Mat. Navuk 1970, No.6, 38-46 (1970). Math. Rev., Vol. 44, 1972, p. 1195, #6557.
R. W. Robinson, Enumeration of Euler graphs, pp. 147-153 of F. Harary, editor, Proof Techniques in Graph Theory. Academic Press, NY, 1969.
R. W. Robinson, personal communication.
R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1979.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Chai Wah Wu, Table of n, a(n) for n = 1..88 (terms 1..60 from Max Alekseyev)
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
Erich Friedman, Illustration of initial terms
V. A. Liskovec, Enumeration of Euler Graphs, (in Russian), Akademiia Navuk BSSR, Minsk., 6 (1970), 38-46. (annotated scanned copy)
C. L. Mallows and N. J. A. Sloane, Two-graphs, switching classes and Euler graphs are equal in number, SIAM J. Appl. Math., 28 (1975), 876-880.
C. L. Mallows and N. J. A. Sloane, Two-graphs, switching classes and Euler graphs are equal in number, SIAM J. Appl. Math., 28 (1975), 876-880. [Copy on N. J. A. Sloane's Home Page]
Brendan McKay, Combinatorial Data (Eulerian graphs).
R. W. Robinson, Enumeration of Euler graphs, pp. 147-153 of F. Harary, editor, Proof Techniques in Graph Theory. Academic Press, NY, 1969. (Annotated scanned copy)
Peter Steinbach, Field Guide to Simple Graphs, Volume 1, Part 17 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)
Eric Weisstein's World of Mathematics, Eulerian Graph.

Cf. A002854, A008683.

A002854 = Import["https://oeis.org/A002854/b002854.txt", "Table"][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
EulerInvTransform[A002854] (* Jean-François Alcover, Aug 27 2019, updated Mar 17 2020 *)

from functools import lru_cache
from itertools import combinations
from fractions import Fraction
from math import prod, gcd, factorial
from sympy import mobius, divisors
from sympy.utilities.iterables import partitions
def A003049(n):
    @lru_cache(maxsize=None)
    def b(n): return int(sum(Fraction(1<>1)-1)*r+(q*r*(r-1)>>1) for q, r in p.items())+any(q&1 for q in p),prod(q**r*factorial(r) for q, r in p.items())) for p in partitions(n)))
    @lru_cache(maxsize=None)
    def c(n): return n*b(n)-sum(c(k)*b(n-k) for k in range(1,n))
    return sum(mobius(n//d)*c(d) for d in divisors(n,generator=True))//n # Chai Wah Wu, Jul 03 2024

Let B(x) = g.f. for A002854. Then g.f. A(x) for A003049 satisfies 1 + B(x) = exp(Sum_{n>=1} A(x^n)/n). - Robinson (1969).
Inverse Euler transform of A002854. (This is equivalent to the Robinson formula.) - Franklin T. Adams-Watters, Jul 24 2006
Let B(x) = g.f. for A002854. Then A(x) = Sum_{m >= 1} (mu(m)/m) * log(1 + B(x^m)), where mu(m) = A008683(m). (This is essentially a re-statement of the equation on p. 151 in Robinson (1969).) - Petros Hadjicostas, Feb 24 2021

a(1)-a(26) were computed by R. W. Robinson

More terms from Vladeta Jovovic, Apr 18 2000

A076864 Number of connected loopless multigraphs with n edges.

Original entry on oeis.org

1, 1, 2, 5, 12, 33, 103, 333, 1183, 4442, 17576, 72810, 314595, 1410139, 6541959, 31322474, 154468852, 783240943, 4077445511, 21765312779, 118999764062, 665739100725, 3807640240209, 22246105114743, 132672322938379, 807126762251748

Offset: 0

N. J. A. Sloane, Nov 23 2002

Inverse Euler transform of A050535.

Andrew Howroyd, Table of n, a(n) for n = 0..50
Patrick T. Komiske, Eric M. Metodiev, and Jesse Thaler, Energy flow polynomials: A complete linear basis for jet substructure, arXiv:1712.07124 [hep-ph], 2017.
Tsuyoshi Miezaki, Akihiro Munemasa, Yusaku Nishimura, Tadashi Sakuma, and Shuhei Tsujie, Universal graph series, chromatic functions, and their index theory, arXiv:2403.09985 [math.CO], 2024. See p. 23.
N. J. A. Sloane, Transforms
Gus Wiseman, Non-isomorphic representatives of the unlabeled connected multigraphs counted by the first 5 terms

Row sums of A191646.
Cf. A050535 (multisets), A076865, A076866, A076867.
Cf. A000664, A007718, A054923, A191970, A275421, A317672, A322114, A322137, A322148.

A050535 = Cases[Import["https://oeis.org/A050535/b050535.txt", "Table"], {, }][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
Join[{1}, EulerInvTransform[A050535 // Rest]] (* Jean-François Alcover, Feb 11 2020, updated Mar 17 2020 *)

More terms from Sean A. Irvine, Oct 02 2011
Name and comment swapped by Gus Wiseman, Nov 28 2018
a(0)=1 prepended by Andrew Howroyd, Oct 23 2019

A085549 Number of isomorphism classes of connected 4-regular multigraphs of order n, loops allowed.

Original entry on oeis.org

1, 2, 4, 10, 28, 97, 359, 1635, 8296, 48432, 316520, 2305104, 18428254, 160384348, 1506613063, 15180782537, 163211097958, 1864251304892, 22540603640086, 287577260214946, 3860595341568062, 54397355465967057, 802684717378090204

Offset: 1

Benjamin A. Burton (bab(AT)debian.org), Jul 04 2003

Also the number of different potential face pairing graphs for closed 3-manifold triangulations.

Computed from A129429 by an inverse Euler transform. - R. J. Mathar, Mar 09 2019

B. A. Burton, Minimal triangulations and face pairing graphs, preprint, 2003.

Andrew Howroyd, Table of n, a(n) for n = 1..40
B. A. Burton, Regina (3-manifold topology software).
B. A. Burton, Minimal triangulations and normal surfaces, Ph.D. thesis, University of Melbourne, 2003.
B. A. Burton, Face pairing graphs and 3-manifold enumeration, arXiv:math/0307382 [math.GT], 2003.
B. A. Burton, Enumeration of non-orientable 3-manifolds using face-pairing graphs and union-find, Discrete and Computational Geometry, 38 (2007), 527-571.
R. de Mello Koch, S. Ramgoolam, Strings from Feynman graph counting: Without large N, Phys. Rev. D 85 (2012) 026007
H. Kleinert, A. Pelster, B. Kastening, M. Bachmann, Recursive graphical construction of Feynman diagrams and their multiplicities in Phi^4 and Phi^2*A theory, Phys. Rev. E 62 (2) (2000), 1537 eq (4.20) or arXiv:hep-th/9907168, 1999.
B. Martelli and C. Petronio, Three-manifolds having complexity at most 9, Experiment. Math., Vol. 10 (2001), pp. 207-236
R. J. Mathar, Illustrations

Column k=4 of A333397.

Cf. A129429, A129417, A005967, A129430, A129432, A129434, A129436, A118560.

A129429 = Cases[Import["https://oeis.org/A129429/b129429.txt", "Table"], {, }][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
EulerInvTransform[A129429] (* Jean-François Alcover, Dec 03 2019, updated Mar 17 2020 *)

Inverse Euler transform of A129429.

a(12)-a(16) from Brendan McKay, Apr 15 2007, computed using software at http://users.cecs.anu.edu.au/~bdm/nauty/
Edited by N. J. A. Sloane, Oct 01 2007
a(17)-a(23) from A129429 from Jean-François Alcover, Dec 03 2019

A000608 Number of connected partially ordered sets with n unlabeled elements.

Original entry on oeis.org

1, 1, 1, 3, 10, 44, 238, 1650, 14512, 163341, 2360719, 43944974, 1055019099, 32664984238, 1303143553205, 66900392672168, 4413439778321689

Offset: 0

N. J. A. Sloane, Simon Plouffe, J. A. Wright

K. K.-H. Butler and G. Markowsky, Enumeration of finite topologies, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 169-184.
E. N. Gilbert, A catalog of partially ordered systems, unpublished memorandum, Aug 08, 1961.
G. Melançon, personal communication.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Gunnar Brinkmann and Brendan D. McKay, Counting unlabeled topologies and transitive relations.
G. Brinkmann and B. D. McKay, Counting unlabeled topologies and transitive relations, J. Integer Sequences, Volume 8, 2005.
G. Brinkmann and B. D. McKay, Posets on up to 16 Points [On Brendan McKay's home page]
G. Brinkmann and B. D. McKay, Posets on up to 16 Points, Order 19 (2) (2002) 147-179.
K. K.-H. Butler and G. Markowsky, Enumeration of finite topologies, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 169-184.
K. K.-H. Butler and G. Markowsky, Enumeration of finite topologies, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 169-184. [Annotated scan of pages 180 and 183 only]
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
E. N. Gilbert, A catalog of partially ordered systems, unpublished memorandum, Aug 08, 1961. [Annotated scanned copy]
Henry Sharp, Jr., Quasi-orderings and topologies on finite sets, Proceedings of the American Mathematical Society 17.6 (1966): 1344-1349. [Annotated scanned copy]
N. J. A. Sloane, List of sequences related to partial orders, circa 1972
N. J. A. Sloane, Transforms
Peter Steinbach, Field Guide to Simple Graphs, Volume 4, Part 10 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)
N. L. White, Two letters to N. J. A. Sloane, 1970, with hand-drawn enclosure
Wikipedia, Illustration n=4, Illustration n=5, Illustration n=6" (2021)
J. A. Wright, There are 718 6-point topologies, quasiorderings and transgraphs, Preprint, 1970. [Annotated scanned copy]
J. A. Wright, There are 718 6-point topologies, quasi-orderings and transgraphs, Notices Amer. Math. Soc., 17 (1970), p. 646, Abstract #70T-A106.
J. A. Wright, Two related abstracts, 1970 and 1972 [Annotated scanned copies]
J. A. Wright, Letter to N. J. A. Sloane, Apr 06 1972, listing 18 sequences
Index entries for sequences related to posets

Inverse Euler transform of A000112.

Cf. A263864 (multiset transform), A342500 (refined by rank).

A000112 = Cases[Import["https://oeis.org/A000112/b000112.txt", "Table"], {, }][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
{1} ~Join~ EulerInvTransform[Rest[A000112]] (* Jean-François Alcover, Dec 04 2019, updated Mar 17 2020 *)

More terms from Christian G. Bower, who pointed out connection with A000112, Jan 21 1998 and Dec 12 2001

More terms from Vladeta Jovovic, Jan 04 2006; corrected Jan 15 2006

A076322 Number of connected 3-colorable (i.e., chromatic number <= 3) simple graphs on n nodes.

Original entry on oeis.org

1, 1, 2, 5, 17, 81, 519, 5218, 81677, 2014360, 76140741, 4303246908

Offset: 1

Eric W. Weisstein, Oct 06 2002

Maria Chudnovsky, Jan Goedgebeur, Oliver Schaudt, Mingxian Zhong, Obstructions for three-coloring graphs without induced paths on six vertices, arXiv preprint, arXiv:1504.06979 [math.CO], 2015-2018.
Eric Weisstein's World of Mathematics, n-Colorable Graph

Cf. A005142, A076323, A076324, A076325, A076326, A076327, A076328.

Cf. A076279, A076315, A084269, A126737.

A076315 = Cases[Import["https://oeis.org/A076315/b076315.txt", "Table"], {, }][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
EulerInvTransform[A076315] (* Jean-François Alcover, Sep 25 2019, updated Mar 17 2020 *)

Inverse Euler transform of A076315. - Andrew Howroyd, Dec 02 2018

a(10)-a(11) from Andrew Howroyd, Dec 02 2018

a(12) from Jinyuan Wang, Feb 23 2020

A076323 Number of connected 4-colorable (i.e., chromatic number <= 4) simple graphs on n nodes.

Original entry on oeis.org

1, 1, 2, 6, 20, 107, 801, 10227, 231228, 9708788, 743177051, 100580560531

Offset: 1

Eric W. Weisstein, Oct 06 2002

Maria Chudnovsky, Jan Goedgebeur, Oliver Schaudt, Mingxian Zhong, Obstructions for three-coloring graphs without induced paths on six vertices, arXiv preprint, arXiv:1504.06979 [math.CO], 2015-2018.
Eric Weisstein's World of Mathematics, n-Colorable Graph

Cf. A005142, A076322, A076324, A076325, A076326, A076327, A076328.

Cf. A076280, A076316, A084269, A126738.

A076316 = Cases[Import["https://oeis.org/A076316/b076316.txt", "Table"], {, }][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
EulerInvTransform[A076316] (* Jean-François Alcover, Sep 25 2019, updated Mar 17 2020 *)

Inverse Euler transform of A076316. - Andrew Howroyd, Dec 02 2018

a(10)-a(11) from Andrew Howroyd, Dec 02 2018

a(12) from Sean A. Irvine, Apr 13 2025

A001548 Number of connected linear spaces with n (unlabeled) points.

Original entry on oeis.org

1, 1, 0, 1, 1, 2, 4, 13, 42, 308, 4845, 227613, 28639650

Offset: 0

N. J. A. Sloane

Euler transform is A001200. - Michael Somos, Apr 24 2014

In any linear space any two distinct points belong to exactly one line. A linear space is disconnected if there exists a partition of the points of the space into two subsets such that for any two distinct points in a subset of the partition the unique line they both belong to is completely contained in that subset. - Michael Somos, Apr 24 2014

			a(2) = 0 because the unique linear space on two points can be partitioned into two single point subsets which disconnects the space vacuously. a(5) = 2 because there are two connected linear spaces with 5 points: one has only one line and the other has two lines with three points that intersect in one point that belongs to no other line while the other four points belong to three lines. - _Michael Somos_, Apr 24 2014

L. M. Batten and A. Beutelspacher: The theory of finite linear spaces, Cambridge Univ. Press, 1993 (see the Appendix).
Doyen, Jean; Sur le nombre d'espaces linéaires non isomorphes de n points. Bull. Soc. Math. Belg. 19 1967 421-437.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

J. Doyen, Sur le nombre d'espaces lineaires non isomorphes de n points [Annotated and scanned copy]
Olaf Lechtenfeld, Konrad Schwerdtfeger and Johannes Thürigen, N=4 Multi-Particle Mechanics, WDVV Equation and Roots, SIGMA 7 (2011), 023. See the table on p. 18 for the sequence a(n)-1 for n > 2.
Pierre Robillard, On the weighted finite linear spaces, Bull. Soc. Math. Belg. 22 (1970), 227-241. [Annotated and scanned copy]

Cf. A001200, A056642.

A001200 = Cases[Import["https://oeis.org/A001200/b001200.txt", "Table"], {, }][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
{1} ~Join~ EulerInvTransform[A001200 // Rest] (* Jean-François Alcover, Jan 04 2020, updated Mar 17 2020 *)

More terms could be obtained from A056642. - N. J. A. Sloane, Jul 26 2004
a(10)-a(12) from A001200. - Michael Somos, Apr 24 2014
a(12) corrected by Jean-François Alcover, Jan 04 2020

cp's OEIS Frontend

A300913 Number of non-isomorphic connected set-systems of weight n.

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A056156 Number of connected bipartite graphs with n edges, no isolated vertices and a distinguished bipartite block, up to isomorphism.

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A002905 Number of connected graphs with n edges.

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A003049 Number of connected Eulerian graphs with n unlabeled nodes.

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A076864 Number of connected loopless multigraphs with n edges.

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A085549 Number of isomorphism classes of connected 4-regular multigraphs of order n, loops allowed.

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A000608 Number of connected partially ordered sets with n unlabeled elements.

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