A261833 a(n) = sum(stirling2(n,k)*(k+1)!*(k+3)!,k=1..n)/48.

1, 16, 406, 14866, 740026, 48026266, 3937533706, 397912444666, 48589663862026, 7053101481134266, 1200393616793282506, 236747809664852265466, 53564655768153719942026, 13780851677757681289022266, 4000515700684222714620799306, 1301419578177153109817779142266, 471541578407011294721978551670026

Offset: 1

Author

Karol A. Penson and Katarzyna Gorska, Oct 02 2015

Keywords

• nonn

Comments

It appears that for all n>1 the last digit of a(n) is 6.

Programs

Maple

with(combinat): a:= n-> sum(stirling2(n, k)*(k+1)!*(k+3)!, k=1..n)/48: seq(a(n), n=1..20);

Mathematica

Table[Sum[StirlingS2[n, k]*(k+1)!*(k+3)!, {k, 1, n}]/48, {n, 1, 20}] (* Vaclav Kotesovec, Oct 05 2015 *)

Formula

Representation as a sum of infinite series of special values of hypergeometric functions of type 2F0, in Maple notation:

a(n) = sum(k^n*(k+1)!*(k+3)!*hypergeom([k+2,k+4],[],-1)/k!, k=1..infinity)/48, n=1,2,... .

a(n) ~ exp(1/2) * (n+1)! * (n+3)! / 48. - Vaclav Kotesovec, Oct 05 2015