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A300520 Expansion of Product_{k>=1} 1 / (1 - Fibonacci(k)*x^k). 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

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.

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A191497 A052325 A302774 * A243082 A092603 A298533

Adjacent sequences:  A300517 A300518 A300519 * A300521 A300522 A300523

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 08 2018

STATUS

approved

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Last modified October 20 15:29 EDT 2019. Contains 328267 sequences. (Running on oeis4.)