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 A130406 #5 Jun 13 2015 10:34:41
%S A130406 1,3,13,83,814,12502,303102,11681388,718217460,70660085940,
%T A130406 11145552305760,2823029266531680,1149529177121700960,
%U A130406 753213189796615454400,794745942920930023732800
%N A130406 Column 1 of triangle A130405.
%F A130406 a(n) = F(n+2)*a(n-1) + F(n+1)*A003266(n+1), where A003266(n) is the product of the first n nonzero Fibonacci numbers (A000045) and F(n) = A000045(n).
%F A130406 a(n) = A003266(n+1)*[ F(n+1) + F(n+2)*Sum_{k=0..n} F(k)/F(k+1) ] where F(n)=A000045(n) is the n-th Fibonacci number.
%e A130406 a(n) = A003266(n+1)*[F(n+1) + F(n+2)*[1+ 1/2+ 2/3+ 3/5+...+ F(n)/F(n+1)]]:
%e A130406 a(3) = 1*1*2*3*( 3 + 5*(1/1 + 1/2 + 2/3) ) = 83;
%e A130406 a(4) = 1*1*2*3*5*( 5 + 8*(1/1 + 1/2 + 2/3 + 3/5) ) = 814;
%e A130406 a(5) = 1*1*2*3*5*8*( 8 + 13*(1/1 + 1/2 + 2/3 + 3/5 + 5/8) ) = 12502.
%o A130406 (PARI) a(n)=polcoeff(prod(i=0,n+1,fibonacci(i+1)+x*fibonacci(i)),1)
%o A130406 (PARI) /* Recurrence a(n) = F(n+2)*a(n-1) + F(n+1)*A003266(n+1): */ a(n)=if(n==0,1,fibonacci(n+2)*a(n-1)+fibonacci(n+1)*prod(i=1,n+1,fibonacci(i)))
%o A130406 (PARI) a(n)=prod(i=1,n+1,fibonacci(i))*(fibonacci(n+1) + fibonacci(n+2)*sum(k=0,n,fibonacci(k)/fibonacci(k+1)))
%Y A130406 Cf. A130405, A130407, A003266, A000045.
%K A130406 nonn
%O A130406 0,2
%A A130406 _Paul D. Hanna_, May 24 2007, May 25 2007