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 A358436 #7 Nov 16 2022 09:44:41
%S A358436 1,2,8,45,322,2730,26004,268554,2940080,33635316,398300344,4849845000,
%T A358436 60429982144,767721774800,9916427702880,129937069996965,
%U A358436 1724052965464890,23129299114182030,313351935000465900,4282621342230699930,58994556159403576140,818487022124443918740
%N A358436 a(n) = Sum_{j=0..n} C(n)*C(n-j), where C(n) is the n-th Catalan number.
%F A358436 a(n) = C(n)*(C(n)*hypergeom([1, -n - 1], [1/2 - n], 1/4) + 1/2).
%F A358436 a(n) = ((-64*n^3 + 160*n^2 - 112*n + 24)*a(n-2) + (20*n^3 - 14*n^2 + 2*n)*a(n-1)) / (n*(n + 1)^2).
%p A358436 C := n -> binomial(2*n, n)/(n + 1):
%p A358436 A358436 := n -> add(C(n)*C(n-j), j = 0..n):
%p A358436 seq(A358436(n), n = 0..21);
%Y A358436 Cf. A000108, A358437.
%K A358436 nonn
%O A358436 0,2
%A A358436 _Peter Luschny_, Nov 16 2022