A023430 Generalized Catalan Numbers.

1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 7, 11, 17, 27, 44, 72, 118, 194, 320, 528, 871, 1439, 2385, 3965, 6605, 11017, 18399, 30771, 51538, 86440, 145165, 244085, 410890, 692442, 1168114, 1972470, 3333834, 5639888, 9549311, 16181931, 27442827, 46575013

Offset

0,9

Links

Table of n, a(n) for n=0..41.

Formula

G.f. A(x) satisfies: A(x) = (1 + x^4 * A(x)^2) / (1 - x + x^4 + x^5 + x^6 + x^7). - Ilya Gutkovskiy, Jul 20 2021

Maple

A023430 := proc(n)
    option remember;
    if n = 0 then
        1;
    else
        procname(n-1)+add(procname(k)*procname(n-4-k), k=4..n-4) ;
    end if;
end proc: # R. J. Mathar, May 01 2015

Mathematica

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

Crossrefs

Cf. A000108, A001006, A004148, A006318.

Sequence in context: A289010 A006999 A005252 * A023429 A023428 A093911

Adjacent sequences: A023427 A023428 A023429 * A023431 A023432 A023433

Keyword

nonn,easy

Author

Olivier Gérard

Extensions

More terms from Sean A. Irvine, Jun 04 2019

Status

approved