A285339 Expansion of Product_{k>=0} (1 + x^(4*k+3))^(4*k+3).

1, 0, 0, 3, 0, 0, 3, 7, 0, 1, 21, 11, 0, 21, 54, 15, 7, 96, 122, 19, 74, 311, 217, 44, 351, 768, 367, 209, 1227, 1663, 591, 989, 3402, 3225, 1156, 3609, 8289, 5815, 3053, 11096, 18015, 10176, 9466, 29593, 36249, 18454, 28960, 71093, 68438, 37297, 81606

Offset: 0

Author

Seiichi Manyama, Apr 17 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Product_{k>=0} (1 + x^(m*k+m-1))^(m*k+m-1): A262736 (m=2), A262948 (m=3), this sequence (m=4), A285340 (m=5).

Cf. A285213, A285311.

Formula

a(n) = (-1)^n * A285213(n).

a(n) ~ exp(3^(4/3) * Zeta(3)^(1/3) * n^(2/3) / 4) * Zeta(3)^(1/6) / (2^(23/24) * 3^(1/3) * sqrt(Pi) * n^(2/3)). - Vaclav Kotesovec, Nov 10 2017