A285262 Expansion of Product_{k>=1} ((1-x^(4*k))/(1-x^k))^k.

1, 1, 3, 6, 12, 23, 45, 80, 145, 256, 446, 761, 1292, 2154, 3568, 5842, 9485, 15261, 24386, 38647, 60867, 95212, 148052, 228860, 351899, 538186, 819105, 1240704, 1870886, 2808888, 4199880, 6254577, 9279179, 13715740, 20202040, 29654210, 43386131, 63274874

Offset: 0

Author

Vaclav Kotesovec, Apr 15 2017

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A026007, A263346, A285263.

Cf. A285215.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Product[((1-x^(4*k))/(1-x^k))^k, {k,1,nmax}], {x,0,nmax}], x]

Formula

a(n) ~ exp(3^(4/3) * (5*Zeta(3))^(1/3) * n^(2/3) / 4) * (5*Zeta(3))^(1/6) / (2^(7/6) * 3^(1/3)* sqrt(Pi) * n^(2/3)).