A351334 a(n) = Sum_{k=0..n} k! * (-k)^k * Stirling2(n,k).

1, -1, 7, -139, 5227, -317491, 28352347, -3495615859, 568791063547, -118065959980051, 30445266606199387, -9547490385298102579, 3578014749635903623867, -1579193384981544127824211, 810752966831581612807206427, -479049438742420410992820125299

Offset: 0

Author

Seiichi Manyama, Feb 07 2022

Keywords

• sign

Crossrefs

Cf. A122399, A351218, A351281, A351333.

Programs

PARI

a(n) = sum(k=0, n, k!*(-k)^k*stirling(n, k, 2));

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*(1-exp(x)))^k)))

Formula

E.g.f.: Sum_{k>=0} (k * (1 - exp(x)))^k.