A347021 - OEIS

A347021

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

1, 1, 4, 32, 364, 5444, 100520, 2210760, 56406240, 1637877600, 53327583360, 1924096475520, 76198487927040, 3285955396558080, 153273199794071040, 7689131281851770880, 412809183978447306240, 23616192920003184176640, 1434201753814306170808320

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..18.

FORMULA

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

a(n) ~ n! * exp(1/16) / (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} (-1)^(k-1) * (4 - 3*k/n) * (k-1)! * binomial(n,k) * a(n-k). - Seiichi Manyama, Sep 11 2023

MATHEMATICA

nmax = 18; CoefficientList[Series[1/(1 - 4 Log[1 + x])^(1/4), {x, 0, nmax}], x] Range[0, nmax]!

Table[Sum[StirlingS1[n, k] 4^k Pochhammer[1/4, k], {k, 0, n}], {n, 0, 18}]

CROSSREFS

Cf. A006252, A007696, A320343, A346983, A347016, A347020, A347022, A347023.

Sequence in context: A224993 A357407 A319220 * A051489 A375949 A295257

Adjacent sequences: A347018 A347019 A347020 * A347022 A347023 A347024

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Aug 11 2021

STATUS

approved