A244451 E.g.f.: exp( Sum_{n>=1} Fibonacci(2*n)*x^n/n ).

1, 1, 4, 26, 236, 2756, 39376, 665464, 12986416, 287394416, 7112021696, 194607175136, 5834321568064, 190181750900416, 6697115871398656, 253362903806266496, 10248299242094541056, 441359565949128552704, 20163160035504969573376, 973917774772339989408256

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..380

Formula

E.g.f.: ( (1 - x/Phi^2) / (1 - Phi^2*x) )^(sqrt(5)/5) where Phi = (sqrt(5)+1)/2.

E.g.f.: exp( Integral 1/(1-3*x+x^2) dx ).

a(n) ~ n! * 5^(1/(2*sqrt(5))) * n^(1/sqrt(5)-1) * ((1+sqrt(5))/2)^(2*n-2/sqrt(5)) / GAMMA(1/sqrt(5)). - Vaclav Kotesovec, Jun 28 2014

Example

E.g.f.: A(x) = 1 + x + 4*x^2/2! + 26*x^3/3! + 236*x^4/4! + 2756*x^5/5! +...
where
log(A(x)) = x + 3*x^2/2 + 8*x^3/3 + 21*x^4/4 + 55*x^5/5 + 144*x^6/6 + 377*x^7/7 + 987*x^8/8 +...+ A000045(2*n)*x^n/n +...

Prog

(PARI) {a(n)=n!*polcoeff(exp(intformal(1/(1-3*x+x^2 +x*O(x^n)))), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A244430, A000045.

Sequence in context: A054360 A124824 A000311 * A001863 A300698 A244524

Adjacent sequences: A244448 A244449 A244450 * A244452 A244453 A244454

Keyword

nonn

Author

Paul D. Hanna, Jun 28 2014

Status

approved