A347016 Expansion of e.g.f. 1 / (1 + 4 * log(1 - x))^(1/4).

1, 1, 6, 62, 916, 17644, 419360, 11859840, 388965600, 14514046560, 607165485120, 28143329181120, 1431690475207680, 79302863940387840, 4751108622148907520, 306118435580577146880, 21107196651940518551040, 1550773243761690603179520, 120947288498720390755353600

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..360

Formula

a(n) = Sum_{k=0..n} |Stirling1(n,k)| * A007696(k).

a(n) ~ n! * exp(n/4) / (Gamma(1/4) * 2^(1/2) * n^(3/4) * (exp(1/4) - 1)^(n + 1/4)). - Vaclav Kotesovec, Aug 14 2021

a(0) = 1; a(n) = Sum_{k=1..n} (4 - 3*k/n) * (k-1)! * binomial(n,k) * a(n-k). - Seiichi Manyama, Sep 09 2023

Maple

g:= proc(n) option remember; `if`(n<2, 1, (4*n-3)*g(n-1)) end:
a:= n-> add(abs(Stirling1(n, k))*g(k), k=0..n):
seq(a(n), n=0..18);  # Alois P. Heinz, Aug 10 2021

Mathematica

nmax = 18; CoefficientList[Series[1/(1 + 4 Log[1 - x])^(1/4), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Abs[StirlingS1[n, k]] 4^k Pochhammer[1/4, k], {k, 0, n}], {n, 0, 18}]

Crossrefs

Cf. A007696, A007840, A346978, A346983, A347015.

Sequence in context: A190726 A121251 A352071 * A222079 A158987 A374227

Adjacent sequences: A347013 A347014 A347015 * A347017 A347018 A347019

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 10 2021

Status

approved