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 A110490 #8 Aug 29 2017 16:07:06
%S A110490 1,1,3,7,20,59,185,600,2003,6833,23727,83606,298313,1076155,3920823,
%T A110490 14416987,53482012,200151737,755894009,2882782933,11115015138,
%U A110490 43400057683,172016505877,694208585423,2863726993748,12130698802645
%N A110490 Diagonal sums of a triangle based on the Catalan numbers.
%C A110490 Diagonal sums of A110488.
%H A110490 G. C. Greubel, <a href="/A110490/b110490.txt">Table of n, a(n) for n = 0..675</a>
%F A110490 a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..(n-2*k)} 2*(j+1)*(k-1)^j*C(2*(n-2*k)+1, n-2*k-j)/(n-2*k+j+2).
%t A110490 T[n_, 0] := CatalanNumber[n]; T[n_, 1] := CatalanNumber[n]; T[n_, n_] := 1; T[n_, k_] := Sum[2*(j + 1)*(k - 1)^j*Binomial[2 (n - k) + 1, n - k - j]/(n - k + j + 2), {j, 0, n - k}]; Join[{1, 1}, Table[Sum[T[n - k, k], {k, 0, n}], {n,2,50}]] (* _G. C. Greubel_, Aug 29 2017 *)
%Y A110490 Cf. A110488.
%K A110490 easy,nonn
%O A110490 0,3
%A A110490 _Paul Barry_, Jul 22 2005