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 A139376 #7 Oct 20 2016 02:42:27
%S A139376 1,1,3,5,11,23,54,136,374,1103,3441,11186,37472,128325,446834,1576251,
%T A139376 5618950,20204874,73190075,266810125,978044403,3602795670,13329486459,
%U A139376 49509151332,184540129492,690061739789,2587941606367,9731587992993
%N A139376 Expansion of 1/((1-x^2*c(x))(1-x-x^2)) where c(x) is the g.f. of A000108.
%C A139376 Diagonal sums of the Fibonacci-Catalan triangle A139375.
%H A139376 G. C. Greubel, <a href="/A139376/b139376.txt">Table of n, a(n) for n = 0..500</a>
%F A139376 a(n) = Sum_{k=0..n} F(k+1)*A132364(n-k).
%F A139376 Conjecture: (-n+1)*a(n) +6*(n-2)*a(n-1) +4*(-2*n+5)*a(n-2) +2*(-n+1)*a(n-3) +3*(3*n-7)*a(n-4) +3*(-n+3)*a(n-5) +2*(-2*n+5)*a(n-6)=0. - _R. J. Mathar_, Feb 05 2015
%t A139376 g[0]:= 1; g[n_]:= Sum[(i/(n - i))*Binomial[2*n - 3*i - 1, n - 2*i], {i, 0, Floor[n/2]}]; a[n_] := Sum[Fibonacci[k + 1]*g[n - k], {k, 0, n}]; Table[a[n], {n, 0, 25}] (* _G. C. Greubel_, Oct 20 2016 *)
%K A139376 easy,nonn
%O A139376 0,3
%A A139376 _Paul Barry_, Apr 15 2008