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 A111262 #25 Mar 03 2024 14:20:18
%S A111262 3,12,65,403,2652,17889,121859,833260,5706081,39096531,267936188,
%T A111262 1836369217,12586419075,86267964108,591287758337,4052742230419,
%U A111262 27777897084444,190392509164065,1304969593244291,8944394450283436
%N A111262 a(n) = (1/n)*Sum_{k=1..n} F(4*k)*B(2*n-2*k)*binomial(2*n,2*k), where F are Fibonacci numbers and B are Bernoulli numbers.
%C A111262 Values are always integers.
%H A111262 Indranil Ghosh, <a href="/A111262/b111262.txt">Table of n, a(n) for n = 1..1194</a>
%H A111262 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (10, -23, 10, -1).
%F A111262 a(n) = F(4*n-2) + 2*F(2*n-1).
%F A111262 Recurrence: a(n) = 10*a(n-1) - 23*a(n-2) + 10*a(n-3) - a(n-4).
%F A111262 O.g.f.: -x*(-3+18*x-14*x^2+x^3)/((x^2-3*x+1)*(x^2-7*x+1)) = -1+(2-4*x)/(x^2-3*x+1)+(-1+8*x)/(x^2-7*x+1). - _R. J. Mathar_, Nov 23 2007
%F A111262 a(n) = (Lucas(2*n-1)+2)*Fibonacci(2*n-1) = A162483(n-1)*A001519(n). - _Ehren Metcalfe_, Jun 04 2019
%t A111262 Table[(1/n)*Sum[Fibonacci[4k]BernoulliB[2n-2k]Binomial[2n,2k],{k,1,n}],{n,1,20}] (* or *) Table[Fibonacci[4n-2]+2Fibonacci[2n-1],{n,1,20}] (* or *) LinearRecurrence[{10,-23,10,-1},{3,12,65,403},20] (* _Indranil Ghosh_, Feb 26 2017 *)
%o A111262 (PARI) a(n)=fibonacci(4*n-2)+2*fibonacci(2*n-1)
%Y A111262 Cf. A001519.
%K A111262 nonn
%O A111262 1,1
%A A111262 _Benoit Cloitre_, Nov 12 2005, corrected Feb 24 2008