A023428 - OEIS

%I #16 Jul 20 2021 19:00:07

%S 1,1,1,1,1,1,2,4,7,11,17,27,45,77,132,224,378,640,1093,1881,3250,5622,

%T 9732,16874,29332,51126,89313,156283,273842,480474,844220,1485472,

%U 2617335,4617243,8154289,14415869,25511256,45190366,80124434,142189496

%N Generalized Catalan Numbers.

%F a(0)=1; a(n) = a(n-1) + Sum_{k=2..n-4} a(k)*a(n-4-k).

%F 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 := proc(n)

%p     option remember;

%p     if n = 0 then

%p         1 ;

%p     else

%p         procname(n-1)+add(procname(k)*procname(n-4-k),k=2..n-4) ;

%p     end if;

%p end proc:

%p seq(A023428(n),n=0..80) ; # _R. J. Mathar_, Oct 31 2014

%t 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 Cf. A000108, A001006, A004148, A006318.

%K nonn,easy

%O 0,7

%A _Olivier Gérard_

%E More terms from _Sean A. Irvine_, Jun 04 2019