A303135 Expansion of Product_{n>=1} (1 - (16*x)^n)^(-1/4).

1, 4, 104, 1760, 39520, 590720, 14285056, 205151232, 4596467200, 75375073280, 1504196046848, 23673049726976, 525315968712704, 7912159583600640, 158055039529779200, 2726833423421800448, 51889395654107463680, 840470097284214292480, 16765991910040314839040

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) = 1/4, g(n) = 16^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), this sequence (b=4), A303136 (b=5).

Cf. A303131, A303153.

Programs

Mathematica

CoefficientList[Series[1/QPochhammer[16*x]^(1/4), {x, 0, 20}], x] (* Vaclav Kotesovec, Apr 19 2018 *)

Formula

a(n) ~ exp(sqrt(n/6)*Pi) * 2^(4*n - 33/16) / (3^(5/16) * n^(13/16)). - Vaclav Kotesovec, Apr 19 2018