A327042 Expansion of Product_{k>=1} 1/((1 - x^k) * (1 - x^(2*k)) * (1 - x^(3*k))).

1, 1, 3, 5, 10, 15, 29, 42, 72, 107, 170, 246, 382, 541, 807, 1139, 1650, 2292, 3267, 4479, 6261, 8518, 11716, 15771, 21449, 28599, 38430, 50876, 67654, 88854, 117171, 152775, 199785, 258901, 336024, 432744, 558027, 714494, 915555, 1166243, 1485792, 1883031

Offset: 0

Author

Vaclav Kotesovec, Aug 16 2019

Keywords

• nonn

Comments

Differs from A006168.

Links

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

Crossrefs

Cf. A000041, A002513, A327043, A327044.

Cf. A006171.

Programs

Mathematica

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

Formula

a(n) ~ 11 * exp(sqrt(11*n)*Pi/3) / (48*sqrt(3)*n^(3/2)).