A333125 a(n) = binomial(Fibonacci(n),n).

1, 1, 0, 0, 0, 1, 28, 1716, 203490, 52451256, 29248649430, 36519676207704, 103619293824707388, 681222021538453426360, 10526080837282875691177000, 387340445158332035685509830240, 34306348668342682111244774082795555, 7379087300345635546662027722168990277849

Offset: 0

Author

Vaclav Kotesovec, Mar 08 2020, following a suggestion of Andrew Nelson

Keywords

• nonn

Links

• Andrew Nelson, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A000045, A014070.

Programs

Mathematica

Table[Binomial[Fibonacci[n], n], {n, 0, 20}]

PARI

a(n) = binomial(fibonacci(n), n); \\ Michel Marcus, Mar 10 2020

Formula

a(n) ~ phi^(n^2) * exp(n) / (sqrt(2*Pi) * 5^(n/2) * n^(n + 1/2)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio.