A347020 Expansion of e.g.f. 1 / (1 - 3 * log(1 + x))^(1/3).

1, 1, 3, 18, 150, 1644, 22116, 353856, 6554376, 138001896, 3254445144, 84979363248, 2433814616592, 75858381808416, 2556180134677152, 92597465283789312, 3588434497019272320, 148134619713440384640, 6489652665043455707520, 300712023388466713739520

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{k=0..n} Stirling1(n,k) * A007559(k).

a(n) ~ n! * exp(1/9) / (Gamma(1/3) * 3^(1/3) * n^(2/3) * (exp(1/3) - 1)^(n + 1/3)). - Vaclav Kotesovec, Aug 14 2021

a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k-1) * (3 - 2*k/n) * (k-1)! * binomial(n,k) * a(n-k). - Seiichi Manyama, Sep 11 2023

Mathematica

nmax = 19; CoefficientList[Series[1/(1 - 3 Log[1 + x])^(1/3), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS1[n, k] 3^k Pochhammer[1/3, k], {k, 0, n}], {n, 0, 19}]

Crossrefs

Cf. A006252, A007559, A320343, A335531, A346982, A347015, A347021, A347022, A347023.

Sequence in context: A152409 A200320 A352850 * A371538 A207569 A005412

Adjacent sequences: A347017 A347018 A347019 * A347021 A347022 A347023

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 11 2021

Status

approved