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A349880
Expansion of Sum_{k>=0} x^k/(1 - k^3 * x).
6
1, 1, 2, 10, 93, 1307, 28002, 842196, 33388393, 1717595949, 111931584098, 8979468552886, 872315432217509, 101425775048588759, 13924209725224120770, 2229705716369149960592, 412760812611799202662609, 87644186710319273062637625, 21180850892383599137766296770
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=0..n} k^(3*(n-k)).
a(n) ~ sqrt(2*Pi/3) * (n/LambertW(exp(1)*n))^(1/2 + 3*n - 3*n/LambertW(exp(1)*n)) / sqrt(1 + LambertW(exp(1)*n)). - Vaclav Kotesovec, Dec 04 2021
PROG
(PARI) a(n, s=0, t=3) = sum(k=0, n, k^(t*(n-k)+s));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-k^3*x)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 03 2021
STATUS
approved