A124125 a(n)=(1/(4n))*sum(k=1,n,F(6k)*B(2n-2k)*binomial(2n,2k)) where F=Fibonacci numbers and B=Bernoulli numbers.

2, 19, 245, 3631, 58121, 973843, 16773677, 293759095, 5196109073, 92455824667, 1650850175669, 29537478199039, 529130102195225, 9485447592486691, 170110949757514301, 3051485664370912903, 54745886982174938657

Offset

1,1

Comments

Linear recurrence and empirical g.f. confirmed by more terms. - Ray Chandler, Mar 07 2024

Links

Ray Chandler, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (35, -383, 1465, -1516, 80).

Formula

a(n)=(1/4)*(F(6n-3)+4^n*F(2n-1)+2*5^(n-1))

Empirical G.f.: -x*(68*x^4-597*x^3+346*x^2-51*x+2) / ((5*x-1)*(x^2-18*x+1)*(16*x^2-12*x+1)). [Colin Barker, Dec 01 2012]

Prog

(PARI) a(n)=(1/4)*(fibonacci(6*n-3)+4^n*fibonacci(2*n-1)+2*5^(n-1))

Crossrefs

Cf. A111262.

Sequence in context: A106945 A211886 A125632 * A234505 A239108 A191806

Adjacent sequences: A124122 A124123 A124124 * A124126 A124127 A124128

Keyword

nonn

Author

Benoit Cloitre, Nov 29 2006

Status

approved