A237654 G.f.: exp( Sum_{n>=1} 5*Fibonacci(n-1)*Fibonacci(n+1) * x^n/n ).

1, 0, 5, 5, 25, 49, 150, 365, 990, 2550, 6726, 17550, 46015, 120390, 315275, 825299, 2160775, 5656855, 14809980, 38772875, 101508876, 265753500, 695751900, 1821501900, 4768754125, 12484760124, 32685526625, 85571819345, 224029931845, 586517975725, 1535523995826, 4020054011225, 10524638038410

Offset

0,3

Comments

Compare to the g.f. of A054888.

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

Links

Table of n, a(n) for n=0..32.

Index entries for linear recurrences with constant coefficients, signature (0,5,5,0,-1).

Formula

G.f.: 1 / ( (1-3*x+x^2) * (1+x)^3 ).

a(n) = (2*Lucas(2*n+5) + (28+25*n+5*n^2)*(-1)^(n))/50 where Lucas = A000032. - Greg Dresden, Jan 01 2021

Example

G.f.: A(x) = 1 + 5*x^2 + 5*x^3 + 25*x^4 + 49*x^5 + 150*x^6 + 365*x^7 + ...
where the logarithm begins:
log(A(x)) = 5*1*2*x^2/2 + 5*1*3*x^3/3 + 5*2*5*x^4/4 + 5*3*8*x^5/5 + 5*5*13*x^6/6 + 5*8*21*x^7/7 + 5*13*34*x^8/8 + ...

Prog

(PARI) {a(n)=polcoeff(exp(sum(m=1, n, 5*fibonacci(m-1)*fibonacci(m+1)*x^m/m) + x*O(x^n)), n)}
for(n=0, 36, print1(a(n), ", "))

Crossrefs

Cf. A237655, A054888, A000032.

Sequence in context: A245520 A245130 A263872 * A038247 A263798 A257607

Adjacent sequences: A237651 A237652 A237653 * A237655 A237656 A237657

Keyword

nonn

Author

Paul D. Hanna, May 05 2014

Status

approved