A345729 Expansion of Product_{k>=1} (1 + x^k + x^(k+2)).

1, 1, 1, 3, 3, 6, 7, 11, 15, 20, 28, 36, 50, 62, 86, 105, 141, 175, 226, 283, 358, 446, 557, 691, 852, 1055, 1286, 1587, 1918, 2353, 2830, 3445, 4134, 4993, 5977, 7174, 8555, 10220, 12138, 14436, 17092, 20232, 23896, 28158, 33172, 38937, 45736, 53512, 62662

Offset: 0

Author

Vaclav Kotesovec, Jun 25 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A160571.

Programs

Mathematica

nmax = 60; CoefficientList[Series[Product[1 + x^k + x^(k+2), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ c * exp(r*sqrt(n)) / n^(3/4), where r = 2*sqrt(-polylog(2,-2)) and c = (-polylog(2,-2))^(1/4) / (6*sqrt(3*Pi)).