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A023428
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Generalized Catalan Numbers.
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1
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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)
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OFFSET
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0,7
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LINKS
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Table of n, a(n) for n=0..33.
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FORMULA
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a(0)=1. a(n) = a(n-1)+sum_{k=2..n-4} a(k)*a(n-4-k).
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MAPLE
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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
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MATHEMATICA
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Clear[ a ]; a[ 0 ]=1; a[ n_Integer ] := a[ n ]=a[ n-1 ]+Sum[ a[ k ]*a[ n-4-k ], {k, 2, n-4} ];
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CROSSREFS
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Cf. A000108, A001006, A004148, A006318.
Sequence in context: A005252 A023430 A023429 * A093911 A152398 A023427
Adjacent sequences: A023425 A023426 A023427 * A023429 A023430 A023431
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KEYWORD
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nonn,easy
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AUTHOR
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Olivier Gérard
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STATUS
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approved
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