This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A124125 #9 Mar 07 2024 12:55:26 %S A124125 2,19,245,3631,58121,973843,16773677,293759095,5196109073,92455824667, %T A124125 1650850175669,29537478199039,529130102195225,9485447592486691, %U A124125 170110949757514301,3051485664370912903,54745886982174938657 %N 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. %C A124125 Linear recurrence and empirical g.f. confirmed by more terms. - _Ray Chandler_, Mar 07 2024 %H A124125 Ray Chandler, <a href="/A124125/b124125.txt">Table of n, a(n) for n = 1..1000</a> %H A124125 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (35, -383, 1465, -1516, 80). %F A124125 a(n)=(1/4)*(F(6n-3)+4^n*F(2n-1)+2*5^(n-1)) %F A124125 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] %o A124125 (PARI) a(n)=(1/4)*(fibonacci(6*n-3)+4^n*fibonacci(2*n-1)+2*5^(n-1)) %Y A124125 Cf. A111262. %K A124125 nonn %O A124125 1,1 %A A124125 _Benoit Cloitre_, Nov 29 2006