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%I #22 Jul 20 2021 07:00:11
%S 1,1,1,1,1,2,4,8,16,32,65,133,274,568,1184,2481,5223,11042,23434,
%T 49908,106633,228505,490999,1057683,2283701,4941502,10713941,23272929,
%U 50642017,110377543,240944076,526717211,1152996206,2527166334,5545804784,12184053993
%N Generalized Catalan Numbers.
%H Seiichi Manyama, <a href="/A023421/b023421.txt">Table of n, a(n) for n = 0..2795</a>
%F G.f. A(x) satisfies: A(x) = (1 + x^2 * A(x)^2) / (1 - x + x^2 + x^3 + x^4). - _Ilya Gutkovskiy_, Jul 20 2021
%p A023421 := proc(n)
%p option remember;
%p if n = 0 then
%p 1;
%p else
%p procname(n-1)+add(procname(k)*procname(n-2-k), k=3..n-2) ;
%p end if;
%p end proc: # _R. J. Mathar_, May 01 2015
%t a[0]=1; a[n_]:= a[n]=a[n-1] + Sum[a[k]*a[n-2-k], {k,3,n-2}]; Table[a[n], {n,0,30}] (* modified by _G. C. Greubel_, Jan 01 2018 *)
%o (PARI) {a(n) = if(n==0,1, a(n-1) + sum(k=3,n-2, a(k)*a(n-k-2)))};
%o for(n=0,30, print1(a(n), ", ")) \\ _G. C. Greubel_, Jan 01 2018
%Y Cf. A000108, A001006, A004148, A004149, A023422, A023423.
%Y Fourth row of A064645.
%K nonn,easy
%O 0,6
%A _Olivier Gérard_
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