A038205 -id:A038205 - cp's OEIS frontend

A098639 Consider the family of directed multigraphs enriched by the species of odd sets. Sequence gives number of those multigraphs with n labeled arcs.

1, 1, 6, 69, 1230, 30663, 1005692, 41571127, 2099861244, 126607647073, 8945129371976, 729628409684925, 67868881258920424, 7125522244948969319, 837004398237510194704, 109173596976047915341823, 15708090522743045757716496, 2478722722731315203268137729

Offset: 0

N. J. A. Sloane, Oct 26 2004

nonn

G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

Andrew Howroyd, Table of n, a(n) for n = 0..200
G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

Cf. A014505, A098623, A098636, A098637, A098638.

\\ EnrichedGdSeq defined in A098623.
EnrichedGdSeq(sinh(x + O(x*x^20))) \\ Andrew Howroyd, Jan 12 2021

E.g.f.: B(sinh(x)) where B(x) is the e.g.f. of A014505. - Andrew Howroyd, Jan 12 2021

Terms a(12) and beyond from Andrew Howroyd, Jan 12 2021

A099692 Consider the family of multigraphs enriched by the species of directed sets. Sequence gives number of those multigraphs with n labeled edges.

Original entry on oeis.org

1, 1, 4, 23, 220, 3016, 55011, 1265824, 35496711, 1183686987, 46072834777, 2062557088117, 104926356851165, 6004962409831577, 383331023991407286, 27094756978689827593, 2107021273883402908850, 179261681391054814324774, 16602830645109035036038335

Offset: 0

N. J. A. Sloane, Oct 26 2004

nonn

G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

Andrew Howroyd, Table of n, a(n) for n = 0..100
G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

Cf. A000110, A014500, A098620, A099693, A099694, A099695.

\\ R(n) is e.g.f. of 1,1,2,2,2,2,...; EnrichedGnSeq defined in A098620.
R(n)={2*exp(x + O(x*x^n)) - x - 1}
EnrichedGnSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

E.g.f.: B(2*exp(x) - x - 2) where B(x) is the e.g.f. of A014500. - Andrew Howroyd, Jan 12 2021

Terms a(11) and beyond from Andrew Howroyd, Jan 12 2021

A099693 Consider the family of multigraphs enriched by the species of directed sets. Sequence gives number of those multigraphs with n loops and edges.

Original entry on oeis.org

1, 2, 11, 89, 1063, 17099, 352700, 8987170, 275303298, 9930027149, 414883314611

Offset: 0

N. J. A. Sloane, Oct 26 2004

nonn

G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

A099694 Consider the family of directed multigraphs enriched by the species of directed sets. Sequence gives number of those multigraphs with n labeled loops and arcs.

Original entry on oeis.org

1, 2, 17, 244, 5283, 156092, 5954547, 282221828, 16159327961, 1094056231572, 86116276633357, 7773114989571400, 795480206815177651, 91417037615848058160, 11701283925663217478843, 1656436690705751478232180, 257730676653629520748175377, 43837005194184348815823808500

Offset: 0

N. J. A. Sloane, Oct 26 2004

nonn

G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

Andrew Howroyd, Table of n, a(n) for n = 0..100
G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

Cf. A014507, A098622, A099692, A099693, A099695.

\\ R(n) is e.g.f. of 1, 1, 2, 2, 2, ...; EnrichedGdlSeq defined in A098622.
R(n)={2*exp(x + O(x*x^n)) - x - 1}
EnrichedGdlSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

E.g.f.: B(2*exp(x) - x - 2) where B(x) is the e.g.f. of A014507. - Andrew Howroyd, Jan 12 2021

Terms a(11) and beyond from Andrew Howroyd, Jan 12 2021

A099695 Consider the family of directed multigraphs enriched by the species of directed sets. Sequence gives number of those multigraphs with n labeled arcs.

Original entry on oeis.org

1, 1, 8, 106, 2144, 59844, 2173450, 98648246, 5433864078, 355229741266, 27080154837658, 2373310690810690, 236327564463489838, 26475199136060717618, 3308794737926514931894, 457980967372496137472590, 69761664006643652403884218, 11629282648335699139979015070

Offset: 0

N. J. A. Sloane, Oct 26 2004

nonn

G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

Andrew Howroyd, Table of n, a(n) for n = 0..100
G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

Cf. A014505, A098623, A099692, A099693, A099694.

\\ R(n) is e.g.f. of 1, 1, 2, 2, 2, ...; EnrichedGdSeq defined in A098623.
R(n)={2*exp(x + O(x*x^n)) - x - 1}
EnrichedGdSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

E.g.f.: B(2*exp(x) - x - 2) where B(x) is the e.g.f. of A014505. - Andrew Howroyd, Jan 12 2021

Terms a(11) and beyond from Andrew Howroyd, Jan 12 2021

A099696 Consider the family of multigraphs enriched by the species of involutions. Sequence gives number of those multigraphs with n labeled edges.

Original entry on oeis.org

1, 1, 4, 25, 244, 3380, 62133, 1440382, 40673705, 1364815169, 53415511305, 2402797049419, 122751622204827, 7051227704802797, 451598420376965588, 32013004761567761223, 2495936511077175475140, 212840593118800653411004, 19753575434503894710824531

Offset: 0

N. J. A. Sloane, Oct 26 2004

nonn

G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

Andrew Howroyd, Table of n, a(n) for n = 0..100
G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

Cf. A000085, A014500, A098620, A099697, A099698, A099699.

\\ R(n) is A000085 as e.g.f.; EnrichedGnSeq defined in A098620.
R(n)={exp(x+x^2/2 + O(x*x^n))}
EnrichedGnSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

E.g.f.: B(R(x)) where B(x) is the e.g.f. of A014500 and 1 + R(x) is the e.g.f. of A000085. - Andrew Howroyd, Jan 12 2021

Terms a(11) and beyond from Andrew Howroyd, Jan 12 2021

A099697 Consider the family of multigraphs enriched by the species of involutions. Sequence gives number of those multigraphs with n loops and edges.

Original entry on oeis.org

1, 2, 11, 93, 1135, 18567, 387976, 9991794, 308837454, 11225560583, 472141867849

Offset: 0

N. J. A. Sloane, Oct 26 2004

nonn

G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

A099698 Consider the family of directed multigraphs enriched by the species of involutions. Sequence gives number of those multigraphs with n labeled loops and arcs.

Original entry on oeis.org

1, 2, 17, 248, 5403, 160420, 6142567, 291996934, 16759322733, 1136940595762, 89641455771637, 8102778995663368, 830222723124364047, 95509354134959796556, 12236166882713532940611, 1733521075683722202738222, 269910543278748394820341769, 45936441912756036235229989058

Offset: 0

N. J. A. Sloane, Jun 25 2017

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..100
G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

Cf. A000085, A014507, A098622, A099696, A099697, A099699.

\\ R(n) is A000085 as e.g.f.; EnrichedGdlSeq defined in A098622.
R(n)={exp(x+x^2/2 + O(x*x^n))}
EnrichedGdlSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

E.g.f.: B(R(x)) where B(x) is the e.g.f. of A014507 and 1 + R(x) is the e.g.f. of A000085. - Andrew Howroyd, Jan 12 2021

Dead sequence restored, corrected and extended by Andrew Howroyd, Jan 12 2021

A099699 Consider the family of directed multigraphs enriched by the species of involutions. Sequence gives number of those multigraphs with n labeled arcs.

Original entry on oeis.org

1, 1, 8, 108, 2200, 61708, 2249268, 102377404, 5651999688, 370171228504, 28262385542832, 2480108374814480, 247231765611893504, 27722619251007202720, 3467475213036160205984, 480277499859342401636704, 73202023124111697153718080, 12209186681659842887207280448

Offset: 0

N. J. A. Sloane, Oct 26 2004

nonn

G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

Andrew Howroyd, Table of n, a(n) for n = 0..100
G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

Cf. A000085, A014505, A098623, A099696, A099697, A099698.

\\ R(n) is A000085 as e.g.f.; EnrichedGdSeq defined in A098623.
R(n)={exp(x+x^2/2 + O(x*x^n))}
EnrichedGdSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

E.g.f.: B(R(x)) where B(x) is the e.g.f. of A014505 and 1 + R(x) is the e.g.f. of A000085. - Andrew Howroyd, Jan 12 2021

Terms a(11) and beyond from Andrew Howroyd, Jan 12 2021

A365974 Expansion of e.g.f. exp( Sum_{k>=0} x^(5k+3) / (5k+3) ).

Original entry on oeis.org

1, 0, 0, 2, 0, 0, 40, 0, 5040, 2240, 0, 1663200, 246400, 479001600, 605404800, 44844800, 699941088000, 274450176000, 355699625881600, 836634972096000, 156436600320000, 1437392253237248000, 1021561084051200000, 1124111547465274368000

Offset: 0

Seiichi Manyama, Sep 23 2023

nonn

Cf. A038205, A130915, A365973.

Cf. A365982.

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=0, N\5, x^(5*k+3)/(5*k+3)))))

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-3)/5)} a(n-5*k-3)/(n-5*k-3)!.

cp's OEIS Frontend

A098639 Consider the family of directed multigraphs enriched by the species of odd sets. Sequence gives number of those multigraphs with n labeled arcs.

Views

Author

Keywords

References

Links

Crossrefs

Programs

PARI

Formula

Extensions

A099692 Consider the family of multigraphs enriched by the species of directed sets. Sequence gives number of those multigraphs with n labeled edges.

Views

Author

Keywords

References

Links

Crossrefs

Programs

PARI

Formula

Extensions

A099693 Consider the family of multigraphs enriched by the species of directed sets. Sequence gives number of those multigraphs with n loops and edges.

Views

Author

Keywords

References

Links

A099694 Consider the family of directed multigraphs enriched by the species of directed sets. Sequence gives number of those multigraphs with n labeled loops and arcs.

Views

Author

Keywords

References

Links

Crossrefs

Programs

PARI

Formula

Extensions

A099695 Consider the family of directed multigraphs enriched by the species of directed sets. Sequence gives number of those multigraphs with n labeled arcs.

Views

Author

Keywords

References

Links

Crossrefs

Programs

PARI

Formula

Extensions

A099696 Consider the family of multigraphs enriched by the species of involutions. Sequence gives number of those multigraphs with n labeled edges.

Views

Author

Keywords

References

Links

Crossrefs

Programs

PARI

Formula

Extensions

A099697 Consider the family of multigraphs enriched by the species of involutions. Sequence gives number of those multigraphs with n loops and edges.

Views

Author

Keywords

References

Links

A099698 Consider the family of directed multigraphs enriched by the species of involutions. Sequence gives number of those multigraphs with n labeled loops and arcs.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

Extensions

A099699 Consider the family of directed multigraphs enriched by the species of involutions. Sequence gives number of those multigraphs with n labeled arcs.

Views

A365974 Expansion of e.g.f. exp( Sum_{k>=0} x^(5k+3) / (5k+3) ).