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 A130407 #5 Jun 13 2015 10:33:34
%S A130407 1,3,9,37,233,2254,34342,827262,31730508,1943441460,190609515540,
%T A130407 29988517246560,7579307667005280,3080578207713982560,
%U A130407 2015291663362285214400,2123462159890867147060800
%N A130407 A diagonal of triangle A130405.
%F A130407 a(n) = F(n+1)*a(n-1) + F(n+2)*A003266(n), where A003266(n) is the product of the first n nonzero Fibonacci numbers (A000045) and F(n) = A000045(n).
%F A130407 a(n) = A003266(n)*[ F(n+2) + F(n+1)*Sum_{k=0..n} F(k+1)/F(k) ] where F(n)=A000045(n) is the n-th Fibonacci number.
%e A130407 a(n) = A003266(n)*[F(n+2) + F(n+1)*[1+ 2/1+ 3/2+ 5/3+...+ F(n+1)/F(n)]]:
%e A130407 a(3) = 1*1*2*( 5 + 3*(1/1 + 2/1 + 3/2) ) = 37;
%e A130407 a(4) = 1*1*2*3*( 8 + 5*(1/1 + 2/1 + 3/2 + 5/3) ) = 233;
%e A130407 a(5) = 1*1*2*3*5*( 13 + 8*(1/1 + 2/1 + 3/2 + 5/3 + 8/5) ) = 2254.
%o A130407 (PARI) a(n)=polcoeff(prod(i=0,n+1,fibonacci(i+1)+x*fibonacci(i)),n)
%o A130407 (PARI) /* Recurrence a(n) = F(n+1)*a(n-1) + F(n+2)*A003266(n): */ {a(n)=if(n==0,1,fibonacci(n+1)*a(n-1)+fibonacci(n+2)*prod(i=1,n,fibonacci(i)))}
%o A130407 (PARI) a(n)=prod(i=1,n,fibonacci(i))*(fibonacci(n+2) + fibonacci(n+1)*sum(k=1,n,fibonacci(k+1)/fibonacci(k)) )
%Y A130407 Cf. A130405, A130406, A003266, A000045.
%K A130407 nonn
%O A130407 0,2
%A A130407 _Paul D. Hanna_, May 24 2007, May 25 2007