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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, 8154289, 14415869, 25511256, 45190366, 80124434, 142189496 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,7
LINKS
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
Sequence in context: A005252 A023430 A023429 * A093911 A152398 A023427
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, Jun 04 2019
STATUS
approved

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Last modified May 18 16:47 EDT 2024. Contains 372664 sequences. (Running on oeis4.)