OFFSET
0,2
REFERENCES
G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.
LINKS
Muniru A Asiru, Table of n, a(n) for n = 0..50
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]
FORMULA
a(n) = Sum_{k=0..n} Stirling1(n, k)*Bell(2*k). - Vladeta Jovovic, Jun 21 2003
E.g.f.: exp(-1)*Sum_{n>=0} (1+x)^(n^2)/n!. - Paul D. Hanna, Jul 03 2011
a(n) = n!*exp(-1)*Sum_{k>=sqrt(n)} binomial(k^2,n)/k!. - Paul D. Hanna, Jul 03 2011
MAPLE
A014507 := proc(n)
add(combinat[stirling1](n, k)*combinat[bell](2*k), k=0..n) ;
end proc:
seq(A014507(n), n=0..10) ; # R. J. Mathar, Apr 30 2017
MATHEMATICA
a[n_] := Sum[StirlingS1[n, k]*BellB[2*k], {k, 0, n}];
Table[a[n], {n, 0, 14}] (* Jean-François Alcover, Jan 21 2018, from Vladeta Jovovic's formula *)
PROG
(PARI) /* From Vladeta Jovovic's formula: */
{Stirling1(n, k)=n!*polcoeff(binomial(x, n), k)}
{Bell(n)=n!*polcoeff(exp(exp(x+x*O(x^n))-1), n)}
{a(n)=sum(k=0, n, Stirling1(n, k)*Bell(2*k))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Simon Plouffe, Gilbert Labelle (gilbert(AT)lacim.uqam.ca)
STATUS
approved