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 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. 1
 2, 19, 245, 3631, 58121, 973843, 16773677, 293759095, 5196109073, 92455824667, 1650850175669, 29537478199039, 529130102195225, 9485447592486691, 170110949757514301, 3051485664370912903, 54745886982174938657 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified July 22 12:38 EDT 2024. Contains 374499 sequences. (Running on oeis4.)