A300520 Expansion of Product_{k>=1} 1 / (1 - Fibonacci(k)*x^k).

1, 1, 2, 4, 8, 15, 31, 57, 113, 212, 410, 757, 1464, 2684, 5083, 9380, 17569, 32120, 59977, 109193, 202046, 367951, 675541, 1224453, 2243795, 4052369, 7377243, 13314989, 24140198, 43406515, 78510429, 140800279, 253663615, 454352111, 815790813, 1457485309

Offset: 0

Author

Vaclav Kotesovec, Mar 08 2018

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..4500

Crossrefs

Cf. A000045, A023882, A075900, A077365, A179381, A318248.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Product[1/(1-Fibonacci[k]*x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

log(a(n)) ~ log(phi)*n + 2*sqrt(polylog(2, 1/sqrt(5))*n) - 3*(log(n)/4), where polylog(2, 1/sqrt(5)) = 0.5107013915606224266804289751265205446721... and phi = A001622 = (1 + sqrt(5))/2 is the golden ratio.