A351504 Expansion of e.g.f. 1/(1 + x^3 * log(1 - x)).

1, 0, 0, 0, 24, 60, 240, 1260, 48384, 423360, 3844800, 38253600, 896797440, 14322147840, 216997522560, 3350656108800, 74820944056320, 1621271286835200, 34293811249152000, 727304513980262400, 18147791755697356800, 476653146551318016000

Offset

0,5

Links

Seiichi Manyama, Table of n, a(n) for n = 0..436

Formula

a(0) = 1; a(n) = n! * Sum_{k=4..n} 1/(k-3) * a(n-k)/(n-k)!.

a(n) = n! * Sum_{k=0..floor(n/4)} k! * |Stirling1(n-3*k,k)|/(n-3*k)!.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x^3*log(1-x))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i!*sum(j=4, i, 1/(j-3)*v[i-j+1]/(i-j)!)); v;
(PARI) a(n) = n!*sum(k=0, n\4, k!*abs(stirling(n-3*k, k, 1))/(n-3*k)!);

Crossrefs

Cf. A052830, A351503.

Cf. A351506, A353229.

Sequence in context: A356911 A353229 A366777 * A356099 A356971 A370995

Adjacent sequences: A351501 A351502 A351503 * A351505 A351506 A351507

Keyword

nonn

Author

Seiichi Manyama, May 04 2022

Status

approved