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 A108478 #12 Sep 27 2014 19:05:46
%S A108478 1,1,2,14,43,127,468,1596,5253,17917,60918,205194,694287,2351611,
%T A108478 7951336,26894840,91004105,307854073,1041410602,3523170438,
%U A108478 11918842803,40320750711,136404504124,461454010164,1561085306061,5281113937653
%N A108478 Diagonal sums of number triangle A108477.
%F A108478 a(n) = sum_{k=0..floor(n/2)} ( sum_{j=0..n-k} C(2(n-2k), j)*C(2k, j)*2^j ).
%F A108478 Empirical g.f.: -(3*x^3+x^2+x-1) / ((x^3-3*x^2-x-1)*(x^3+x^2+3*x-1)). - _Colin Barker_, Sep 26 2014
%p A108478 A108478:=n->add(add(binomial(2*(n-2*k),j)*binomial(2*k,j)*2^j, j=0..n-k), k=0..floor(n/2)): seq(A108478(n), n=0..30); # _Wesley Ivan Hurt_, Sep 26 2014
%t A108478 Table[Sum[Sum[Binomial[2 (n - 2 k), j]*Binomial[2 k, j]*2^j, {j, 0, n - k}], {k, 0, Floor[n/2]}], {n, 0, 30}] (* _Wesley Ivan Hurt_, Sep 26 2014 *)
%o A108478 (PARI) a(n) = sum(k=0, n\2, sum(j=0, n-k, binomial(2*(n-2*k), j)*binomial(2*k, j)*2^j)); \\ _Michel Marcus_, Sep 26 2014
%K A108478 easy,nonn
%O A108478 0,3
%A A108478 _Paul Barry_, Jun 04 2005