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A375949
Expansion of e.g.f. 1 / (4 - 3 * exp(x))^(4/3).
4
1, 4, 32, 368, 5520, 102064, 2242832, 57095728, 1652211600, 53559908784, 1922581295632, 75700072208688, 3243905700776080, 150289130386531504, 7485459789379535632, 398857142195958963248, 22639650637589839298960, 1363772478150606703714224
OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} A007559(k+1) * Stirling2(n,k).
a(n) ~ 3 * sqrt(Pi) * n^(n + 5/6) / (2^(13/6) * Gamma(1/3) * log(4/3)^(n + 4/3) * exp(n)). - Vaclav Kotesovec, Sep 06 2024
MATHEMATICA
nmax=17; CoefficientList[Series[1 / (4 - 3 * Exp[x])^(4/3), {x, 0, nmax}], x]*Range[0, nmax]! (* Stefano Spezia, Sep 03 2024 *)
PROG
(PARI) a007559(n) = prod(k=0, n-1, 3*k+1);
a(n) = sum(k=0, n, a007559(k+1)*stirling(n, k, 2));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 03 2024
STATUS
approved