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A207971
G.f.: exp( Sum_{n>=1} 5*Fibonacci(n)^(2*n) * x^n/n ).
4
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.
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 22 2012
STATUS
approved