A023428 Generalized Catalan Numbers.

1, 1, 1, 1, 1, 1, 2, 4, 7, 11, 17, 27, 45, 77, 132, 224, 378, 640, 1093, 1881, 3250, 5622, 9732, 16874, 29332, 51126, 89313, 156283, 273842, 480474, 844220, 1485472, 2617335, 4617243, 8154289, 14415869, 25511256, 45190366, 80124434, 142189496

Offset

0,7

Links

Table of n, a(n) for n=0..39.

Formula

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

G.f. A(x) satisfies: A(x) = (1 + x^4 * A(x)^2) / (1 - x + x^4 + x^5). - Ilya Gutkovskiy, Jul 20 2021

Maple

A023428 := proc(n)
    option remember;
    if n = 0 then
        1 ;
    else
        procname(n-1)+add(procname(k)*procname(n-4-k), k=2..n-4) ;
    end if;
end proc:
seq(A023428(n), n=0..80) ; # R. J. Mathar, Oct 31 2014

Mathematica

Clear[ a ]; a[ 0 ]=1; a[ n_Integer ] := a[ n ]=a[ n-1 ]+Sum[ a[ k ]*a[ n-4-k ], {k, 2, n-4} ];

Crossrefs

Cf. A000108, A001006, A004148, A006318.

Sequence in context: A005252 A023430 A023429 * A093911 A152398 A023427

Adjacent sequences: A023425 A023426 A023427 * A023429 A023430 A023431

Keyword

nonn,easy

Author

Olivier Gérard

Extensions

More terms from Sean A. Irvine, Jun 04 2019

Status

approved