A278680 Expansion of Product_{n>=1} (1 - x^(5*n))/(1 - x^n)^4 in powers of x.

1, 4, 14, 40, 105, 251, 570, 1226, 2540, 5075, 9855, 18630, 34439, 62340, 110805, 193624, 333235, 565415, 947040, 1567130, 2564425, 4152535, 6658711, 10579380, 16663755, 26033200, 40357641, 62106290, 94912385, 144088840, 217368655, 325945320, 485950150, 720515475

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f.: Product_{n>=1} (1 - x^(5*n))/(1 - x^n)^4.

a(n) ~ 19 * exp(Pi*sqrt(38*n/15)) / (120 * sqrt(10) * n^(3/2)). - Vaclav Kotesovec, Nov 10 2017

Example

G.f.: 1 + 4*x + 14*x^2 + 40*x^3 + 105*x^4 + 251*x^5 + 570*x^6 + ...

Mathematica

nmax = 30; CoefficientList[Series[Product[(1 - x^(5*k))/(1 - x^k)^4, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2017 *)

Crossrefs

Cf. Product_{n>=1} (1 - x^(5*n))/(1 - x^n)^k: A035959 (k=1), A160461 (k=2), A278668 (k=3), this sequence (k=4), A277212 (k=5), A182821 (k=6).

Sequence in context: A066368 A274327 A160463 * A121593 A160527 A023003

Adjacent sequences: A278677 A278678 A278679 * A278681 A278682 A278683

Keyword

nonn

Author

Seiichi Manyama, Nov 25 2016

Status

approved