OFFSET
0,3
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 11 2021
STATUS
approved