A380370 Expansion of e.g.f. log( 1 - log(1 - x)^5 / 120 ).

0, 0, 0, 0, 0, 1, 15, 175, 1960, 22449, 269199, 3410000, 45753180, 650179816, 9771920158, 155020511282, 2589903552600, 45462951235584, 836599468436514, 16102788580144350, 323508284210923974, 6770014833358706076, 147290030512050486060, 3325319844639779998836

Offset: 0

Author

Seiichi Manyama, Jan 23 2025

Keywords

• nonn

Crossrefs

Cf. A346966, A377376, A379674.

Programs

PARI

a(n) = sum(k=1, n\5, (-1)^(k-1)*(5*k)!*abs(stirling(n, 5*k, 1))/(k*120^k));

Formula

a(n) = Sum_{k=1..floor(n/5)} (-1)^(k-1) * (5*k)! * |Stirling1(n,5*k)|/(k * 120^k).

a(n) = |Stirling1(n,5)| - Sum_{k=1..n-1} |Stirling1(k,5)| * binomial(n-1,k) * a(n-k).