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A347015 Expansion of e.g.f. 1 / (1 + 3 * log(1 - x))^(1/3). 6
1, 1, 5, 42, 498, 7644, 144156, 3225648, 83536008, 2457701928, 80970232104, 2953056534768, 118112744060208, 5140622709134496, 241863782829704928, 12232551538417012992, 661818290353375962240, 38140594162828447248000, 2332567001993176540206720, 150880256846462633823648000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=0..n} |Stirling1(n,k)| * A007559(k).
a(n) ~ n! * exp(n/3) / (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} (3 - 2*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, (3*n-2)*g(n-1)) end:
a:= n-> add(abs(Stirling1(n, k))*g(k), k=0..n):
seq(a(n), n=0..19); # Alois P. Heinz, Aug 10 2021
MATHEMATICA
nmax = 19; CoefficientList[Series[1/(1 + 3 Log[1 - x])^(1/3), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Abs[StirlingS1[n, k]] 3^k Pochhammer[1/3, k], {k, 0, n}], {n, 0, 19}]
CROSSREFS
Cf. A354263.
Sequence in context: A317352 A352069 A355786 * A102693 A052654 A108398
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 10 2021
STATUS
approved

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Last modified April 14 14:52 EDT 2024. Contains 371665 sequences. (Running on oeis4.)