A262960 a(n) = sum(stirling2(n,k)*(k+2)!*(k+3)!, k=1..n)/144.

1, 21, 661, 28941, 1678501, 124467021, 11484880261, 1290503997741, 173495416001701, 27499205820027021, 5075028072491665861, 1078923766195953890541, 261780612944688782844901, 71901410584558939807059021, 22195276604290979611365107461, 7651037112318147566092161607341

Offset: 1

Author

Karol A. Penson and Katarzyna Gorska, Oct 05 2015

Keywords

• nonn

Comments

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

Crossrefs

Cf. A261833.

Programs

Maple

with(combinat): a:= n-> sum(stirling2(n, k)*(k+2)!*(k+3)!, k=1..n)/144: seq(a(n), n=1..20);

Mathematica

Table[Sum[StirlingS2[n, k] (k + 2)! (k + 3)!, {k, n}]/144, {n, 16}] (* Michael De Vlieger, Oct 05 2015 *)

Formula

Representation as a sum of infinite series of special values of hypergeometric functions of type 2F0, in Maple notation: sum(k^n*(k+2)!*(k+3)!*hypergeom([k+3,k+4],[],-1)/k!, k=1..infinity)/144, n=1,2... .

a(n) ~ exp(1/2) * (n+2)! * (n+3)! / 144. - Vaclav Kotesovec, Oct 05 2015