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 A108296 #10 Sep 02 2024 21:57:00
%S A108296 1,1,2,3,5,8,14,24,43,78,144,269,509,971,1868,3618,7049,13805,27162,
%T A108296 53661,106405,211697,422458,845386,1696017,3410522,6873060,13878721,
%U A108296 28077439,56900936,115501012,234807488,478032437,974507543,1989123814
%N A108296 Diagonal sums of the number triangle associated to A086617.
%C A108296 The triangle associated to A086617 is given by T(n,k)=if(k<=n, sum{j=0..n-k, C(n-k,j)C(k,j)C(j)},0). A050253(n)=A108296(n+2)-A108296(n).
%F A108296 G.f.: (1-x^2-sqrt(1-2*x^2-4*x^3-3*x^4))/(2*x^3*(1-x^2)).
%F A108296 a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..n-2*k} binomial(n-2*k, j)*binomial(k, j) * A000108(j).
%F A108296 Conjecture: (n+3)*a(n) +(-n-2)*a(n-1) +2*(-n-1)*a(n-2) +2*(-n+3)*a(n-3) +(n+1)*a(n-4) +3*(n-2)*a(n-5)=0. - _R. J. Mathar_, Nov 16 2012
%K A108296 easy,nonn
%O A108296 0,3
%A A108296 _Paul Barry_, May 31 2005