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A277974 Expansion of ((Product_{n>=1} (1 - x^(5*n))/(1 - x^n)^5) - 1)/5 in powers of x. 7
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 (list; graph; refs; listen; history; text; internal format)
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: A024450 A047094 A145128 * A089092 A181527 A049611

Adjacent sequences:  A277971 A277972 A277973 * A277975 A277976 A277977

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Nov 07 2016

STATUS

approved

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Last modified December 15 03:08 EST 2017. Contains 296020 sequences.