A347003 Expansion of e.g.f. exp( log(1 - x)^4 / 4! ).

1, 0, 0, 0, 1, 10, 85, 735, 6804, 68544, 754130, 9044750, 117773656, 1656897528, 25061576176, 405667844400, 6997383182854, 128126051451184, 2481884332498848, 50702417505257904, 1089371806098805286, 24555007848629510700, 579348221233739760550, 14278529041496660104450

Offset

0,6

Links

Seiichi Manyama, Table of n, a(n) for n = 0..447

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * |Stirling1(k,4)| * a(n-k).

a(n) = Sum_{k=0..floor(n/4)} (4*k)! * |Stirling1(n,4*k)|/(24^k * k!). - Seiichi Manyama, May 06 2022

Mathematica

nmax = 23; CoefficientList[Series[Exp[Log[1 - x]^4/4!], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] Abs[StirlingS1[k, 4]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 23}]

Prog

(PARI) a(n) = sum(k=0, n\4, (4*k)!*abs(stirling(n, 4*k, 1))/(24^k*k!)); \\ Seiichi Manyama, May 06 2022

Crossrefs

Cf. A000454, A327505, A346923, A347001, A347002, A347004.

Sequence in context: A354318 A346946 A000454 * A346923 A145146 A252981

Adjacent sequences: A347000 A347001 A347002 * A347004 A347005 A347006

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 10 2021

Status

approved