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 A358437 #12 Feb 19 2024 04:35:33
%S A358437 1,2,10,75,714,7896,96492,1265550,17496050,251958564,3748716036,
%T A358437 57282665622,895001791740,14249639190000,230568513719400,
%U A358437 3783394404776475,62848104088770450,1055378592304360500,17894108081334292500,306026774743629058350,5274529871824080624900
%N A358437 a(n) = Sum_{j=0..n} binomial(n, j)*C(n)*C(n-j), where C(n) is the n-th Catalan number.
%H A358437 Paolo Xausa, <a href="/A358437/b358437.txt">Table of n, a(n) for n = 0..750</a>
%F A358437 a(n) = C(n)^2*hypergeom([-n - 1, -n], [1/2 - n], -1/4).
%F A358437 a(n) = ((-80*n^3 + 240*n^2 - 220*n + 60)*a(n-2) + (24*n^3 - 20*n^2 + 4*n)*a(n-1)) / (n*(n + 1)^2) for n >= 2.
%p A358437 C := n -> binomial(2*n, n)/(n + 1):
%p A358437 A358437 := n -> add(binomial(n, j)*C(n)*C(n-j), j = 0..n):
%p A358437 seq(A358437(n), n = 0..20);
%t A358437 Array[CatalanNumber[#]^2*Hypergeometric2F1[-#-1, -#, 1/2-#, -1/4] &, 25, 0] (* _Paolo Xausa_, Feb 19 2024 *)
%Y A358437 Cf. A000108, A358436.
%K A358437 nonn
%O A358437 0,2
%A A358437 _Peter Luschny_, Nov 16 2022