A350725 a(n) = Sum_{k=0..n} k! * k^(n-k) * Stirling1(n,k).

1, 1, 1, -4, -2, 274, -3442, -12552, 2108664, -63083232, 87416112, 112192496976, -7487840132544, 174521224997040, 19793498724358032, -3109195219736188416, 209306170972547346816, 2973238556525799866496, -3013574861684426837113728, 456220653756733889826621696

Offset: 0

Author

Seiichi Manyama, Feb 03 2022

Keywords

• sign

Crossrefs

Cf. A007840, A229234, A320083, A350721, A350726.

Programs

Mathematica

a[0] = 1; a[n_] := Sum[k! * k^(n-k) * StirlingS1[n, k], {k, 1, n}]; Array[a, 20, 0] (* Amiram Eldar, Feb 03 2022 *)

PARI

a(n) = sum(k=0, n, k!*k^(n-k)*stirling(n, k, 1));

PARI

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

Formula

E.g.f.: Sum_{k>=0} log(1 + k*x)^k / k^k.