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

Author

Benoit Cloitre, Nov 29 2006

Keywords

• nonn

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).

Crossrefs

Cf. A111262.

Programs

PARI

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

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]