A277974 Expansion of ((Product_{n>=1} (1 - x^(5*n))/(1 - x^n)^5) - 1)/5 in powers of x.

0, 1, 4, 13, 38, 101, 252, 594, 1340, 2907, 6104, 12447, 24744, 48068, 91476, 170838, 313646, 566824, 1009628, 1774290, 3079338, 5282172, 8962288, 15050848, 25032420, 41255101, 67406472, 109236685, 175654072, 280371510, 444372452, 699579062, 1094289564

Offset

0,3

Links

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

Formula

a(n) = A277212(n)/5, n > 0.

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

a(n) ~ exp(4*Pi*sqrt(n/5)) / (sqrt(2) * 5^(11/4) * n^(7/4)). - Vaclav Kotesovec, Nov 10 2016

Example

G.f. = x + 4*x^2 + 13*x^3 + 38*x^4 + 101*x^5 + 252*x^6 + ...

Mathematica

nmax = 50; CoefficientList[Series[(Product[(1 - x^(5*j))/(1 - x^j)^5, {j, 1, nmax}] - 1)/5, {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2016 *)
a[ n_] := SeriesCoefficient[ (QPochhammer[ x^5] / QPochhammer[ x]^5 - 1) / 5, {x, 0, n}]; (* Michael Somos, Nov 13 2016 *)

Prog

(PARI) x='x+O('x^66); concat([0], Vec(eta(x^5)/eta(x)^5-1)/5) \\ Joerg Arndt, Nov 27 2016

Crossrefs

Cf. Expansion of ((Product_{n>=1} (1 - x^(k*n))/(1 - x^n)^k) - 1)/k in powers of x: A014968 (k=2), A277968 (k=3), this sequence (k=5), A160549 (k=7), A277912 (k=11).

Sequence in context: A047094 A145128 A357286 * A089092 A181527 A049611

Adjacent sequences: A277971 A277972 A277973 * A277975 A277976 A277977

Keyword

nonn

Author

Seiichi Manyama, Nov 07 2016

Status

approved