A349880 Expansion of Sum_{k>=0} x^k/(1 - k^3 * x).

1, 1, 2, 10, 93, 1307, 28002, 842196, 33388393, 1717595949, 111931584098, 8979468552886, 872315432217509, 101425775048588759, 13924209725224120770, 2229705716369149960592, 412760812611799202662609, 87644186710319273062637625, 21180850892383599137766296770

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..246

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

Cf. A026898, A234568, A349881.

Cf. A349857.

Sequence in context: A293709 A063393 A348837 * A260339 A205320 A254243

Adjacent sequences: A349877 A349878 A349879 * A349881 A349882 A349883

Keyword

nonn

Author

Seiichi Manyama, Dec 03 2021

Status

approved