A351506 Expansion of e.g.f. 1/(1 + x^3/6 * log(1 - x)).

1, 0, 0, 0, 4, 10, 40, 210, 2464, 20160, 178800, 1755600, 21215040, 268107840, 3596916960, 51452200800, 800489733120, 13262804755200, 232536822336000, 4300843392518400, 84023034413644800, 1727339274045504000, 37248117171719731200, 840387048760633651200

Offset

0,5

Links

Seiichi Manyama, Table of n, a(n) for n = 0..450

Formula

a(0) = 1; a(n) = n!/6 * 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)|/(6^k * (n-3*k)!).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x^3/6*log(1-x))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i!/6*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))/(6^k*(n-3*k)!));

Crossrefs

Cf. A052830, A351505.

Cf. A351493, A351504,

Sequence in context: A356913 A351493 A368166 * A355995 A356753 A356968

Adjacent sequences: A351503 A351504 A351505 * A351507 A351508 A351509

Keyword

nonn

Author

Seiichi Manyama, May 04 2022

Status

approved