A383050 a(n) = Sum_{k=0..n} (k+1)^6 * Stirling1(n,k).

1, 64, 665, 2037, -1316, -1148, 16400, -116032, 809592, -6059424, 49512792, -442266888, 4302605280, -45351578400, 515054655360, -6268075470720, 81309027784320, -1118525784929280, 16235659302272640, -247395991797912960, 3936073920965890560, -64988868076072657920

Offset: 0

Author

Seiichi Manyama, Apr 14 2025

Keywords

• sign

Comments

Inverse Stirling transform of (n+1)^6.

Links

• Christian G. Bower, PARI programs for transforms, 2007.
• N. J. A. Sloane, Maple programs for transforms, 2001-2020.

Crossrefs

Column k=6 of A383049.

Programs

PARI

a(n) = sum(k=0, n, (k+1)^6*stirling(n, k, 1));

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k+1)^6*log(1+x)^k/k!)))

Formula

E.g.f.: Sum_{k>=0} (k+1)^6 * log(1+x)^k / k!.

E.g.f.: (1+x) * Sum_{k=0..6} Stirling2(7,k+1) * log(1+x)^k.