A261616 Expansion of Product_{k>=0} 1/(1 - x^(3*k+1))^2.

1, 2, 3, 4, 7, 10, 13, 18, 26, 34, 44, 58, 76, 96, 123, 156, 196, 244, 304, 374, 461, 566, 690, 836, 1015, 1224, 1470, 1762, 2110, 2512, 2987, 3542, 4191, 4944, 5825, 6842, 8025, 9392, 10971, 12788, 14891, 17300, 20068, 23242, 26883, 31034, 35787, 41204

Offset

0,2

Comments

Self-convolution of A035382.

In general, if a > 0, b > 0, GCD(a,b) = 1 and g.f. = Product_{k>=0} 1/(1 - x^(a*k+b))^2, then a(n) ~ Gamma(b/a)^2 * a^(b/a - 3/4) * exp(2*Pi*sqrt(n/(3*a))) * Pi^(2*b/a - 2) / (4 * 3^(b/a - 1/4) * n^(b/a + 1/4)).

Links

Table of n, a(n) for n=0..47.

Formula

a(n) ~ exp(2*Pi*sqrt(n)/3) * Gamma(1/3)^2 / (4 * sqrt(3) * Pi^(4/3) * n^(7/12)).

Mathematica

nmax = 60; CoefficientList[Series[Product[1/(1 - x^(3*k+1))^2, {k, 0, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A022567, A035382, A261610, A261612, A261615.

Sequence in context: A073149 A065461 A008824 * A333615 A329774 A081942

Adjacent sequences: A261613 A261614 A261615 * A261617 A261618 A261619

Keyword

nonn

Author

Vaclav Kotesovec, Aug 26 2015

Status

approved