A327043 Expansion of Product_{k>=1} 1/((1 - x^k) * (1 - x^(2*k)) * (1 - x^(3*k)) * (1 - x^(4*k))).

1, 1, 3, 5, 11, 16, 32, 47, 84, 124, 205, 298, 477, 681, 1044, 1484, 2211, 3097, 4516, 6261, 8948, 12295, 17273, 23511, 32597, 43975, 60187, 80601, 109114, 144999, 194423, 256584, 341008, 447178, 589558, 768398, 1005854, 1303450, 1694815, 2184666, 2823229

Offset

0,3

Comments

Differs from A006169.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Formula

a(n) ~ 5^(5/2) * exp(5*Pi*sqrt(n/2)/3) / (288*2^(1/4)*n^(7/4)).

Mathematica

nmax = 50; CoefficientList[Series[Product[1/((1 - x^k) * (1 - x^(2*k)) * (1 - x^(3*k)) * (1 - x^(4*k))), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000041, A002513, A327042, A327044.

Cf. A006171.

Sequence in context: A018313 A219039 A074820 * A006169 A323582 A088328

Adjacent sequences: A327040 A327041 A327042 * A327044 A327045 A327046

Keyword

nonn

Author

Vaclav Kotesovec, Aug 16 2019

Status

approved