A294669 Expansion of Product_{k>=1} 1/(1 - x^(2*k-1))^(k*(3*k-1)/2).

1, 1, 1, 6, 6, 18, 33, 55, 115, 185, 373, 604, 1113, 1903, 3251, 5678, 9350, 16153, 26420, 44561, 72912, 120150, 196329, 317988, 516881, 827778, 1333570, 2120492, 3381947, 5347513, 8447482, 13285450, 20813814, 32547272, 50638328, 78707858, 121738479

Offset

0,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..5000

Formula

a(n) ~ exp(2*Pi * n^(3/4) / (3*5^(1/4)) + Zeta(3) * sqrt(5*n) / Pi^2 + 5^(1/4) * (Pi/48 - 5*Zeta(3)^2 / Pi^5) * n^(1/4) + 100*Zeta(3)^3 / (3*Pi^8) + 17*Zeta(3) / (96*Pi^2) - 1/24) * sqrt(A) / (2^(101/48) * 5^(11/96) * Pi^(1/24) * n^(59/96)), where A is the Glaisher-Kinkelin constant A074962.

Mathematica

nmax = 50; CoefficientList[Series[Product[1/(1-x^(2*k-1))^(k*(3*k-1)/2), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A035528, A262811, A294591, A278768.

Sequence in context: A161787 A342285 A092297 * A224711 A073096 A212622

Adjacent sequences: A294666 A294667 A294668 * A294670 A294671 A294672

Keyword

nonn

Author

Vaclav Kotesovec, Nov 06 2017

Status

approved