A325952 G.f.: 1/(1-x)^4 * Product_{k>=1} (1 + x^k).

1, 5, 15, 36, 75, 142, 251, 421, 677, 1052, 1589, 2343, 3384, 4800, 6701, 9224, 12538, 16850, 22413, 29534, 38584, 50010, 64348, 82238, 104442, 131864, 165573, 206830, 257118, 318176, 392039, 481082, 588070, 716216, 869245, 1051467, 1267860, 1524162, 1826975

Offset

0,2

Comments

In general, if g.f. = 1/(1-x)^m * Product_{k>=1} (1 + x^k), then a(n) ~ 2^(m - 2) * 3^(m/2 - 1/4) * n^(m/2 - 3/4) * exp(Pi*sqrt(n/3)) / Pi^m.

Links

Table of n, a(n) for n=0..38.

Formula

a(n) ~ 4 * 3^(7/4) * n^(5/4) * exp(Pi*sqrt(n/3)) / Pi^4.

Mathematica

nmax = 50; CoefficientList[Series[(1/(1-x)^4 * Product[1+x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A000009, A014161, A036469, A095944, A120477, A292508, A325951.

Sequence in context: A011933 A093802 A006008 * A086716 A046776 A360486

Adjacent sequences: A325949 A325950 A325951 * A325953 A325954 A325955

Keyword

nonn

Author

Vaclav Kotesovec, May 28 2019

Status

approved