A111420 a(n) = Sum_{q=0..n} Stirling2(n+1,q)^2*q!.

0, 1, 19, 315, 6601, 178923, 6161065, 262268499, 13470911521, 818285112123, 57836073876505, 4693152951066099, 432360761046527041, 44794795435021490043, 5176959026638375267225, 662704551819559746282579, 93384393940399990403502241, 14406589076081640590750974203

Offset: 0

Author

N. J. A. Sloane, Nov 14 2005

Keywords

• nonn

Crossrefs

Cf. A023997, A014235.

Programs

Maple

a:= n-> add(Stirling2(n+1,q)^2*q!, q=0..n):
seq(a(n), n=0..19);  # Alois P. Heinz, May 11 2020

Mathematica

Table[Sum[StirlingS2[n+1, k]^2 * k!, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 12 2018 *)