A192552 a(n) = sum(stirling2(n,k)*(-1)^(n-k)*k!^2,k=0..n).

1, 1, 3, 25, 387, 9481, 336723, 16340185, 1038177507, 83616187561, 8323660051443, 1003415542660345, 144043181112445827, 24279259683302736841, 4747993384270354742163, 1066206704980940216628505, 272480888391150986151565347

Offset: 0

Author

Emanuele Munarini, Jul 04 2011

Keywords

• nonn

Programs

Mathematica

Table[Sum[StirlingS2[n,k](-1)^(n-k)k!^2,{k,0,n}],{n,0,100}]

Maxima

makelist(sum(stirling2(n,k)*(-1)^(n-k)*k!^2,k,0,n),n,0,24);

PARI

{a(n)=polcoeff(sum(m=0, n, m!^2*x^m/prod(k=1, m, 1+k*x+x*O(x^n))), n)} /* Paul D. Hanna, Jul 20 2011 */

Formula

O.g.f.: Sum_{n>=0} n!^2 * x^n / Product_{k=0..n} (1 + k*x). [From Paul D. Hanna, Jul 20 2011]

a(n) ~ exp(-1/2) * n!^2. - Vaclav Kotesovec, Jul 05 2021