A346923 Expansion of e.g.f. 1 / (1 - log(1 - x)^4 / 4!).

1, 0, 0, 0, 1, 10, 85, 735, 6839, 69804, 784580, 9680000, 130312336, 1901581968, 29895585356, 503657235900, 9051009737834, 172807817059664, 3493189152511608, 74530548004474584, 1673793045085649146, 39467836062718058100, 974939402596817961050, 25177327470510057799550

Offset

0,6

Links

Seiichi Manyama, Table of n, a(n) for n = 0..441

Formula

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

a(n) ~ n! * 2^(-5/4) * 3^(1/4) / (exp(2^(3/4)*3^(1/4)) * (1 - exp(-2^(3/4)*3^(1/4)))^(n+1)). - Vaclav Kotesovec, Aug 08 2021

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

Mathematica

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

Prog

(PARI) my(x='x+O('x^25)); Vec(serlaplace(1/(1-log(1-x)^4/4!))) \\ Michel Marcus, Aug 07 2021
(PARI) a(n) = sum(k=0, n\4, (4*k)!*abs(stirling(n, 4*k, 1))/24^k); \\ Seiichi Manyama, May 06 2022

Crossrefs

Cf. A007840, A346921, A346922, A346924.

Cf. A000454, A346895, A347003, A353119.

Sequence in context: A346946 A000454 A347003 * A145146 A252981 A184122

Adjacent sequences: A346920 A346921 A346922 * A346924 A346925 A346926

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 07 2021

Status

approved