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 A023428 #21 Feb 03 2025 09:36:47
%S A023428 1,1,1,1,1,1,2,4,7,11,17,27,45,77,132,224,378,640,1093,1881,3250,5622,
%T A023428 9732,16874,29332,51126,89313,156283,273842,480474,844220,1485472,
%U A023428 2617335,4617243,8154289,14415869,25511256,45190366,80124434,142189496
%N A023428 Generalized Catalan Numbers x^4*A(x)^2 -(1-x+x^4+x^5)*A(x) +1 =0.
%F A023428 a(0)=1; a(n) = a(n-1) + Sum_{k=2..n-4} a(k)*a(n-4-k).
%F A023428 G.f. A(x) satisfies: A(x) = (1 + x^4 * A(x)^2) / (1 - x + x^4 + x^5). - _Ilya Gutkovskiy_, Jul 20 2021
%p A023428 A023428 := proc(n)
%p A023428 option remember;
%p A023428 if n = 0 then
%p A023428 1 ;
%p A023428 else
%p A023428 procname(n-1)+add(procname(k)*procname(n-4-k),k=2..n-4) ;
%p A023428 end if;
%p A023428 end proc:
%p A023428 seq(A023428(n),n=0..80) ; # _R. J. Mathar_, Oct 31 2014
%t A023428 Clear[ a ]; a[ 0 ]=1; a[ n_Integer ] := a[ n ]=a[ n-1 ]+Sum[ a[ k ]*a[ n-4-k ], {k, 2, n-4} ];
%Y A023428 Cf. A000108, A001006, A004148, A006318.
%K A023428 nonn,easy
%O A023428 0,7
%A A023428 _Olivier Gérard_
%E A023428 More terms from _Sean A. Irvine_, Jun 04 2019