A367879 Expansion of e.g.f. 1/(1 + 3 * x * log(1-x)).

1, 0, 6, 9, 240, 1170, 25812, 244440, 5464512, 79579584, 1926411120, 37900930320, 1018338863616, 25047229315680, 752077828672128, 22027545026192160, 738063856107279360, 24935406131189352960, 927531711339595204608, 35370336293213512527360

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(0) = 1; a(n) = 3 * n! * Sum_{k=2..n} 1/(k-1) * a(n-k)/(n-k)!.

a(n) = n! * Sum_{k=0..floor(n/2)} 3^k * k! * |Stirling1(n-k,k)|/(n-k)!.

Prog

(PARI) a(n) = n!*sum(k=0, n\2, 3^k*k!*abs(stirling(n-k, k, 1))/(n-k)!);

Crossrefs

Cf. A052830, A367878.

Sequence in context: A375661 A375672 A367881 * A264375 A061110 A110460

Adjacent sequences: A367876 A367877 A367878 * A367880 A367881 A367882

Keyword

nonn

Author

Seiichi Manyama, Dec 03 2023

Status

approved