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 A119359 #14 Sep 13 2024 03:31:17
%S A119359 0,1,1,7,31,106,386,1499,5755,21886,83854,323302,1248534,4828916,
%T A119359 18719364,72711123,282867795,1101981430,4298723990,16788997874,
%U A119359 65641296578,256895812108,1006307847324,3945185527582,15478851119966
%N A119359 Central coefficients of number triangle A119326.
%C A119359 a(n) = A119326(2n,n+1). A119358(n)-a(n) = A071688(n).
%F A119359 G.f.: (1/sqrt(1-4x)+(1/sqrt(1+4x^2)-1)-c(x)+x*c(-x^2))/2, c(x) the g.f. of A000108;
%F A119359 a(n) = (C(2n,n+1)+C((n-1)/2)*sin(Pi*n/2)-2*0^n-2C(n-1,n/2)*sin(Pi*(n-1)/2))/2.
%F A119359 a(n) = hypergeom([-1/2-n/2, 1/2-n/2, 1-n/2, -n/2], [1/2, 1/2, 1], 1) - 0^n. - _Vladimir Reshetnikov_, Oct 04 2016
%t A119359 Table[HypergeometricPFQ[{-1/2 - n/2, 1/2 - n/2, 1 - n/2, -n/2}, {1/2, 1/2, 1}, 1] - KroneckerDelta[n], {n, 0, 20}] (* _Vladimir Reshetnikov_, Oct 04 2016 *)
%t A119359 Table[(2^n Binomial[1/2, (n+1)/2] + Binomial[n, n/2] Cos[Pi n/2] + n CatalanNumber[n])/2 - KroneckerDelta[n], {n, 0, 20}] (* _Vladimir Reshetnikov_, Oct 06 2016 *)
%K A119359 easy,nonn
%O A119359 0,4
%A A119359 _Paul Barry_, May 16 2006