A381025 Expansion of e.g.f. -log(1-x)^3 * exp(x) / (6 * (1-x)).

0, 0, 0, 1, 14, 145, 1415, 14084, 147532, 1646714, 19664350, 251282911, 3430766658, 49928212971, 772465487885, 12671188958674, 219793939324536, 4021442067435092, 77425990864146652, 1565193235764750557, 33153390461212914806, 734397759275046673253, 16982466756411641668051

Offset: 0

Author

Seiichi Manyama, Feb 12 2025

Keywords

• nonn

Crossrefs

Column k=4 of A269951 (with a different offset).

Cf. A381023.

Programs

Mathematica

nmax=22; CoefficientList[Series[-Log[1-x]^3*Exp[x]/(6*(1-x)),{x,0,nmax}],x]Range[0,nmax]! (* Stefano Spezia, Feb 12 2025 *)

PARI

a(n) = sum(k=0, n, binomial(n, k)*abs(stirling(k+1, 4, 1)));

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * |Stirling1(k+1,4)|.

a(n) = A381023(n+1) - A381023(n).