A377376 -id:A377376 - cp's OEIS frontend

A379674 Expansion of e.g.f. -log( 1 - log(1 - x)^4 / 24 ).

0, 0, 0, 0, 1, 10, 85, 735, 6804, 68544, 754130, 9044750, 117779431, 1657347978, 25083122701, 406495546275, 7025691638029, 129034238530984, 2510053743368448, 51563288466007704, 1115617292385725186, 25359995212317017700, 604332959567317283050, 15066452630930326289950

Offset: 0

Seiichi Manyama, Jan 23 2025

nonn

Cf. A346966, A377376, A380370.

a(n) = sum(k=1, n\4, (4*k)!*abs(stirling(n, 4*k, 1))/(k*24^k));

a(n) = Sum_{k=1..floor(n/4)} (4*k)! * |Stirling1(n,4*k)|/(k * 24^k).

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

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

Original entry on oeis.org

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

Seiichi Manyama, Jan 23 2025

nonn

Cf. A346966, A377376, A379674.

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

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).

cp's OEIS Frontend

A379674 Expansion of e.g.f. -log( 1 - log(1 - x)^4 / 24 ).

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