|
|
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
|
Table of n, a(n) for n=0..39.
|
|
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
|
|
EXTENSIONS
|
More terms from Sean A. Irvine, Jun 04 2019
|
|
STATUS
|
approved
|
|
|
|