A303136 Expansion of Product_{n>=1} (1 - (25*x)^n)^(-1/5).

1, 5, 200, 5125, 177500, 3952500, 150715625, 3185187500, 112844843750, 2783033593750, 86330708203125, 2019237027343750, 72195817812500000, 1591910699609375000, 50158322275878906250, 1322261581989501953125, 39183430287559814453125, 946961406814801025390625

Offset: 0

Author

Seiichi Manyama, Apr 19 2018

Keywords

• nonn

Comments

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 1/5, g(n) = 25^n.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..500

Crossrefs

Expansion of Product_{n>=1} (1 - ((b^2)*x)^n)^(-1/b): A000041 (b=1), A271235 (b=2), A271236 (b=3), A303135 (b=4), this sequence (b=5).

Cf. A303132, A303154.

Programs

Mathematica

CoefficientList[Series[1/QPochhammer[25*x]^(1/5), {x, 0, 20}], x] (* Vaclav Kotesovec, Apr 19 2018 *)
CoefficientList[Series[Product[(1-(25x)^n)^(-1/5),{n,20}],{x,0,20}],x] (* Harvey P. Dale, Nov 04 2021 *)

Formula

a(n) ~ exp(Pi*sqrt(2*n/15)) * 5^(2*n - 3/10) / (2^(7/5) * 3^(3/10) * n^(4/5)). - Vaclav Kotesovec, Apr 19 2018