A276519 Expansion of Product_{k>=1} 1/(1 - x^(2*k) - x^(3*k)).

1, 0, 1, 1, 2, 2, 5, 4, 9, 10, 17, 19, 34, 37, 61, 75, 112, 138, 209, 256, 376, 478, 675, 866, 1222, 1566, 2175, 2830, 3873, 5055, 6900, 9011, 12213, 16045, 21599, 28429, 38191, 50290, 67341, 88884, 118669, 156751, 209018, 276200, 367734, 486376, 646688

Offset: 0

Author

Vaclav Kotesovec, Nov 15 2016

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A264905, A266686, A275820, A275821, A276526.

Programs

Mathematica

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

Formula

a(n) ~ c * p / r^n, where r = A075778 = 1/A060006 = 0.7548776662466927600495... is the real root of the equation r^3 + r^2 - 1 = 0, p = Product_{n>1} 1/(1 - r^(2*n) - r^(3*n)) = 3.820450591662541853... and c = 0.41149558866264576338190038... is the real root of the equation -1 + 8*c - 23*c^2 + 23*c^3 = 0.