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A023428 Generalized Catalan Numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Table of n, a(n) for n=0..33.

FORMULA

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

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

STATUS

approved

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Last modified October 22 01:42 EDT 2018. Contains 316431 sequences. (Running on oeis4.)