A023430 Generalized Catalan Numbers x^4*A(x)^2 -(1-x+x^4+x^5+x^6+x^7)*A(x) + 1 =0.

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

Author

Olivier Gérard

Keywords

• nonn
• easy

Crossrefs

Cf. A000108, A001006, A004148, A006318.

Programs

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} ];

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

Extensions

More terms from Sean A. Irvine, Jun 04 2019