A309733 - OEIS

A309733

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

1, 1, 2, 4, 7, 12, 22, 36, 62, 104, 174, 286, 478, 780, 1284, 2100, 3433, 5586, 9114, 14798, 24064, 39050, 63376, 102726, 166584, 269835, 437190, 707964, 1146480, 1855966, 3004748, 4863306, 7871798, 12739576, 20617652, 33364524, 53992834, 87369548, 141379728, 228769842

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..39.

FORMULA

a(n) ~ phi^(n+1), where phi =A001622= (1+sqrt(5))/2 is the golden ratio. -Vaclav Kotesovec,Sep 22 2019

MATHEMATICA

nmax = 40; CoefficientList[Series[Product[1/(1 - x^k/(1 - x^(2*k))), {k, 1, nmax}], {x, 0, nmax}], x] (*Vaclav Kotesovec,Sep 22 2019 *)

PROG

(PARI) N=66; x='x+O('x^N); Vec(1/prod(k=1, N, 1-x^k/(1-x^(2*k))))

CROSSREFS