proposed

approved

editing

proposed

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

Andrew Howroyd, <a href="/A099698/b099698.txt">Table of n, a(n) for n = 0..100</a>

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

(PARI) \\ 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

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

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

Duplicate Consider the family of directed multigraphs enriched by the species of involutions. Sequence gives number of A098622those multigraphs with n labeled arcs and loops.

1, 2, 17, 250, 5465, 162677, 6241059, 297132409, 17075153860, 1159545515804248, 5403, 160420, 6142567, 291996934, 16759322733, 1136940595762, 89641455771637, 8102778995663368, 830222723124364047, 95509354134959796556, 12236166882713532940611, 1733521075683722202738222, 269910543278748394820341769, 45936441912756036235229989058

dead

nonn

approved

editing

editing

approved

G. Paquin, <a href="/A038205/a038205.pdf">Dénombrement de multigraphes enrichis</a>, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

N. J. A. Sloane, Jun 25 2017

approved

editing

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

Duplicate of A098622.

1, 2, 17, 250, 5465, 162677, 6241059, 297132409, 17075153860, 1159545515804, 91501467848088, 8276847825732141, 848577193578286942, 97672164219292005480, 12518933902769241287267, 1774279753092963892540493

G. Paquin, D\'enombrement de multigraphes enrichis, M\'emoire, Math. Dept., Univ. Qu\'ebec \`a Montr\'eal, July 2004.

a(n) = Sum_{k=0..n} Stirling2(n,k)*Bell(2*k). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 15 2006

nonn,new

dead

njas, Oct 26 2004

More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 15 2006

1, 2, 17, 248, 5403, 160420, 6142567, 291996934, 16759322733, 1136940595762, 89641455771637250, 5465, 162677, 6241059, 297132409, 17075153860, 1159545515804, 91501467848088, 8276847825732141, 848577193578286942, 97672164219292005480, 12518933902769241287267, 1774279753092963892540493

a(n) = Sum_{k=0..n} Stirling2(n,k)*Bell(2*k). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 15 2006

More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 15 2006

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

1, 2, 17, 248, 5403, 160420, 6142567, 291996934, 16759322733, 1136940595762, 89641455771637

0,2

G. Paquin, D\'enombrement de multigraphes enrichis, M\'emoire, Math. Dept., Univ. Qu\'ebec \`a Montr\'eal, July 2004.

nonn

njas, Oct 26 2004

approved