A382793 a(n) = Sum_{k=0..n} (-1)^k * (Stirling2(n,k) * k!)^2.

1, -1, 3, -1, -525, 21599, -575757, -11712961, 4147828275, -478419026401, 27474795508083, 3849481231073279, -1772585499434165325, 366912253456842693599, -26525609280231515934477, -17189616925094873258825281, 10414911263566240831226298675, -3136992122810471155294591778401

Offset: 0

Author

Ilya Gutkovskiy, Apr 05 2025

Keywords

• sign

Crossrefs

Cf. A047797, A048144, A192552.

Programs

Mathematica

Table[Sum[(-1)^k (StirlingS2[n, k] k!)^2, {k, 0, n}], {n, 0, 17}]
Table[(n!)^2 SeriesCoefficient[1/(2 - Exp[x] - Exp[y] + Exp[x + y]), {x, 0, n}, {y, 0, n}], {n, 0, 17}]

Formula

a(n) = (n!)^2 * [(x*y)^n] 1 / (2 - exp(x) - exp(y) + exp(x + y)).