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A207969 G.f.: exp( Sum_{n>=1} 5*Fibonacci(n)^4 * x^n/n ). 7
1, 5, 15, 60, 295, 1625, 9430, 56465, 345010, 2139595, 13419500, 84926105, 541398665, 3472389210, 22385362895, 144945232375, 942089445030, 6143582084115, 40181143112035, 263482860974570, 1731780213622125, 11406235045261205, 75268685723935940 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Conjecture: exp( Sum_{n>=1} 5*Fibonacci(n)^(2*k) * x^n/n ) is an integer series for integers k>=0.

Note that exp( Sum_{n>=1} 5*Fibonacci(n)^(2*k+1) * x^n/n ) is not an integer series for integers k.

Note that exp( Sum_{n>=1} Fibonacci(n)^(2*k) * x^n/n ) is not an integer series for integers k.

LINKS

Table of n, a(n) for n=0..22.

FORMULA

The o.g.f. A(x) = 1 + 5*x + 15*x^2 + 60*x^3 + ... is an algebraic function: A(x)^5 = (1 + 3*x + x^2)^4/( (1 - 7*x + x^2)*(1 - 2*x + x^2)^3 ). Cf. A203804. - Peter Bala, Apr 03 2014

EXAMPLE

G.f.: A(x) = 1 + 5*x + 15*x^2 + 60*x^3 + 295*x^4 + 1625*x^5 + 9430*x^6 +...

such that

log(A(x))/5 = x + x^2/2 + 2^4*x^3/3 + 3^4*x^4/4 + 5^4*x^5/5 + 8^4*x^6/6 + 13^4*x^7/7 +...+ Fibonacci(n)^4*x^n/n +...

PROG

(PARI) {a(n)=polcoeff(exp(sum(k=1, n, 5*fibonacci(k)^4*x^k/k)+x*O(x^n)), n)}

for(n=0, 25, print1(a(n), ", "))

CROSSREFS

Cf. A054888, A207970, A207971, A207972, A207834, A207835.

A077916, A203804.

Sequence in context: A149598 A149599 A149600 * A149601 A149602 A149603

Adjacent sequences:  A207966 A207967 A207968 * A207970 A207971 A207972

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 22 2012

STATUS

approved

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Last modified December 5 16:12 EST 2019. Contains 329753 sequences. (Running on oeis4.)