A207971 G.f.: exp( Sum_{n>=1} 5*Fibonacci(n)^(2*n) * x^n/n ).

1, 5, 15, 140, 8795, 9808325, 57315191130, 2812698182891585, 894119494320160426760, 2048089587570930007354766745, 32079229816919862900907520464756250, 3500720882833094608324749707338857577696205, 2633228648869966875007549667526201212159637714889015

Offset

0,2

Comments

Give g.f. A(x), note that A(x)^(1/5) is not an integer series.

Links

Table of n, a(n) for n=0..12.

Example

G.f.: A(x) = 1 + 5*x + 15*x^2 + 140*x^3 + 8795*x^4 + 9808325*x^5 +...
such that
log(A(x))/5 = x + x^2/2 + 2^6*x^3/3 + 3^8*x^4/4 + 5^10*x^5/5 + 8^12*x^6/6 + 13^14*x^7/7 +...+ Fibonacci(n)^(2*n)*x^n/n +...

Prog

(PARI) {a(n)=polcoeff(exp(sum(k=1, n, 5*fibonacci(k)^(2*k)*x^k/k)+x*O(x^n)), n)}
for(n=0, 31, print1(a(n), ", "))

Crossrefs

Cf. A054888, A207969, A207970, A207972, A207834, A207834.

Sequence in context: A116957 A124209 A207970 * A245648 A048347 A034980

Adjacent sequences: A207968 A207969 A207970 * A207972 A207973 A207974

Keyword

nonn

Author

Paul D. Hanna, Feb 22 2012

Status

approved