A355375 a(n) = Sum_{k=0..n} (-k)^(n-k) * Stirling2(n,k).

1, 1, 0, -4, 10, 67, -969, 3341, 86976, -1988704, 14144108, 405611857, -17544321563, 287677263837, 3595470378748, -421298868094940, 14476946230894114, -112253861285434961, -18711849695261432065, 1354595712379990848137, -44436925726445545236496

Offset: 0

Author

Seiichi Manyama, Jun 30 2022

Keywords

• sign

Crossrefs

Cf. A229233, A232549, A318183, A355376.

Programs

Mathematica

a[n_] := Sum[(-k)^(n - k) * StirlingS2[n, k], {k, 0, n}]; a[0] = 1; Array[a, 20, 0] (* Amiram Eldar, Jun 30 2022 *)

PARI

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

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (1-exp(-k*x))^k/(k^k*k!))))

Formula

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