A014500 -id:A014500 - cp's OEIS frontend

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

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

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

A099700 Consider the family of multigraphs enriched by the species of simple graphs. Sequence gives number of those multigraphs with n labeled edges.

Original entry on oeis.org

1, 1, 4, 29, 330, 5438, 128211, 4808964, 378829853, 77137284917, 36854103598061, 36864364745783295, 74684573193253556537, 304187997559381840229969, 2484431769481244742219110666, 40639512967159110848931023115111, 1330529956364528398902155692019721596

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..50
G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

Cf. A006125, A014500, A098620, A099701, A099702, A099703.

\\ R(n) is A006125 as e.g.f.; EnrichedGnSeq defined in A098620.
R(n)={sum(k=0, n, 2^binomial(k,2)*x^k/k!) + 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 A006125. - Andrew Howroyd, Jan 12 2021

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

A099704 Consider the family of multigraphs enriched by the species of directed graphs. Sequence gives number of those multigraphs with n labeled edges.

Original entry on oeis.org

1, 2, 24, 776, 79840, 35397440, 69619053504, 564929183555840, 18464894708236907776, 2418517115222622481308160, 1267747370909677813160722947072, 2658511777246500251150215101758228480, 22300872810108738542496498718468714032205824

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..50
G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

Cf. A002416, A014500, A098620, A099705, A099706, A099707.

\\ R(n) is A002416 as e.g.f.; EnrichedGnSeq defined in A098620.
R(n)={sum(k=0, n, 2^(k^2)*x^k/k!) + O(x*x^n)}
EnrichedGnSeq(R(15)) \\ 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 A002416. - Andrew Howroyd, Jan 12 2021

Terms a(10) and beyond from Andrew Howroyd, Jan 12 2021

A099708 Consider the family of multigraphs enriched by the species of endofunctions. Sequence gives number of those multigraphs with n labeled edges.

Original entry on oeis.org

1, 1, 6, 60, 854, 16029, 378871, 10926690, 375538541, 15097900582, 699359781567, 36859422340308, 2187121403805853, 144804645827958839, 10615679263174481480, 856040905847508506792, 75495130803739278866508, 7244702305184037575057831, 753093536414613689614872227

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. A000312, A014500, A098620, A099709, A099710, A099711.

\\ R(n) is A000312 as e.g.f.; EnrichedGnSeq defined in A098620.
R(n)={1/(1 + lambertw(-x + 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 A000312. - Andrew Howroyd, Jan 12 2021

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

A099712 Consider the family of multigraphs enriched by the species of arborescences. Sequence gives number of those multigraphs with n labeled edges.

Original entry on oeis.org

1, 1, 4, 30, 338, 5169, 101251, 2446806, 71043973, 2429762734, 96364601877, 4375603494478, 225044659552381, 12990629618136191, 834981228656630494, 59346659738963806022, 4635924974380060251228, 395864230878802130389079, 36773114396103232927777067

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. A000169, A014500, A098620, A099713, A099714, A099715.

\\ R(n) is A000169 as e.g.f.; EnrichedGnSeq defined in A098620.
R(n)={-lambertw(-x + 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 R(x) is the e.g.f. of A000169. - Andrew Howroyd, Jan 12 2021

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

A099716 Consider the family of multigraphs enriched by the species of trees. Sequence gives number of those multigraphs with n labeled edges.

Original entry on oeis.org

1, 1, 3, 18, 170, 2244, 38686, 834594, 21874433, 681399298, 24797467947, 1039645748808, 49632586028650, 2671404673776080, 160726892084432840, 10729582290405547592, 789572236551678855603, 63682341168165082629698, 5600777517339868668401105

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. A000272, A014500, A098620, A099717, A099718, A099719.

\\ R(n) is A000272 as e.g.f.; EnrichedGnSeq defined in A098620.
R(n)={my(w=lambertw(-x + O(x*x^n))); 1 - w - w^2/2}
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 A000272. - Andrew Howroyd, Jan 12 2021

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

A020562 Number of cyclic multigraphs on n labeled edges (without loops).

Original entry on oeis.org

1, 1, 3, 17, 152, 1933, 32608, 695657, 18148533, 564860131, 20581455139, 864802010595, 41392831046804, 2233799248861031, 134737655762330602, 9015762313899965851, 664889968074287179739

Offset: 0

Gilbert Labelle (gilbert(AT)lacim.uqam.ca), Simon Plouffe

nonn

G. Labelle, Counting enriched multigraphs according to the number of their edges (or arcs), Discrete Math., 217 (2000), 237-248.
G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

Cf. A014500.

a(n) = Sum_{k=0..n} (-1)^(n-k)*Stirling1(n, k)*A014500(k). - Sean A. Irvine, Apr 25 2019

A192516 Number of line graphs on [1,...,n].

Original entry on oeis.org

1, 1, 2, 8, 62, 739, 11660, 229003, 5487341, 157413957, 5310060277, 207442849742, 9266622204859, 468316344074444, 26534795158872607, 1672482335988644162, 116473621430584439236, 8908899406447047324336, 744489132650874081005467

Offset: 0

N. J. A. Sloane, Jul 03 2011

nonn

Peter Cameron, Thomas Prellberg, Dudley Stark, Asymptotic enumeration of 2-covers and line graphs, Discrete Math. 310 (2010), no. 2, 230-240 (see l_n).

Cf. A014500.

E.g.f. = exp(-x^3/6-x^4/6-x^5/8-x^6/48)*U(x), where U(x) is the e.g.f. for A014500.

cp's OEIS Frontend

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

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

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A099700 Consider the family of multigraphs enriched by the species of simple graphs. Sequence gives number of those multigraphs with n labeled edges.

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A099704 Consider the family of multigraphs enriched by the species of directed graphs. Sequence gives number of those multigraphs with n labeled edges.

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A099708 Consider the family of multigraphs enriched by the species of endofunctions. Sequence gives number of those multigraphs with n labeled edges.

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A099712 Consider the family of multigraphs enriched by the species of arborescences. Sequence gives number of those multigraphs with n labeled edges.

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PARI

Formula

Extensions

A099716 Consider the family of multigraphs enriched by the species of trees. Sequence gives number of those multigraphs with n labeled edges.

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Author

Keywords

References

Links

Crossrefs

Programs

PARI

Formula

Extensions

A020562 Number of cyclic multigraphs on n labeled edges (without loops).

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