A285290 Expansion of Product_{k>=1} ((1 + x^k) / (1 + x^(4*k)))^k.

1, 1, 2, 5, 7, 15, 26, 44, 74, 125, 205, 331, 534, 844, 1332, 2077, 3215, 4934, 7533, 11410, 17191, 25751, 38346, 56833, 83814, 123025, 179776, 261639, 379186, 547476, 787516, 1128775, 1612395, 2295701, 3258177, 4610130, 6503873, 9149365, 12835612, 17959085

Offset: 0

Author

Vaclav Kotesovec, Apr 16 2017

Keywords

• nonn

Links

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

Crossrefs

Cf. A285289, A263345, A285291.

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[((1+x^k)/(1+x^(4*k)))^k, {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ exp(2^(-8/3) * 3^(5/3) * (5*Zeta(3))^(1/3) * n^(2/3)) * (5*Zeta(3))^(1/6) / (2^(4/3) * 3^(1/6) * sqrt(Pi) * n^(2/3)).