A279328 - OEIS

A279328

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

1, 1, 3, 4, 8, 11, 20, 27, 44, 60, 92, 124, 183, 244, 348, 461, 640, 840, 1144, 1488, 1992, 2572, 3393, 4348, 5668, 7212, 9301, 11760, 15024, 18880, 23924, 29892, 37596, 46728, 58376, 72193, 89644, 110340, 136248, 166968, 205115, 250316, 306056, 372032, 452876

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OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: Product_{k>=1} (1 + x^(2*k)) / (1 - x^k).

a(n) ~ sqrt(5/6) * exp(sqrt(5*n/6)*Pi) / (8*n). - Vaclav Kotesovec, Dec 10 2016

EXAMPLE

G.f.: 1 + x + 3*x^2 + 4*x^3 + 8*x^4 + 11*x^5 + 20*x^6 + 27*x^7 + 44*x^8 + ...

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[(1 + x^(2*k)) / (1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Dec 10 2016 *)