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

0,6

Links

Table of n, a(n) for n=0..23.

Formula

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).

Prog

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

Crossrefs

Cf. A346966, A377376, A380370.

Sequence in context: A000454 A384836 A347003 * A346923 A145146 A252981

Adjacent sequences: A379671 A379672 A379673 * A379675 A379676 A379677

Keyword

nonn

Author

Seiichi Manyama, Jan 23 2025

Status

approved