A309172 Expansion of Product_{k>=1} 1/(1 - (1 + x + x^2) * x^k).

1, 1, 3, 7, 15, 31, 64, 128, 254, 496, 961, 1844, 3516, 6662, 12564, 23593, 44153, 82385, 153351, 284857, 528235, 978148, 1809120, 3342722, 6171318, 11385733, 20994298, 38693809, 71288111, 131297855, 241761727, 445068646, 819205061, 1507641487, 2774307387, 5104712633

Offset: 0

Author

Ilya Gutkovskiy, Jul 15 2019

Keywords

• nonn

Crossrefs

Cf. A160571, A227681, A309173.

Programs

Mathematica

nmax = 35; CoefficientList[Series[Product[1/(1 - (1 + x + x^2) x^k), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 35; CoefficientList[Series[Exp[Sum[x^k Sum[(1 + x + x^2)^d/d, {d, Divisors[k]}], {k, 1, nmax}]], {x, 0, nmax}], x]

Formula

G.f.: exp(Sum_{k>=1} x^k * Sum_{d|k} (1 + x + x^2)^d/d).

a(n) ~ 1/((1 + 2*r + 3*r^2) * QPochhammer[r] * r^(n+1)), where r = A192918. - Vaclav Kotesovec, Jul 16 2019