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A130564 Member k=5 of a family of generalized Catalan numbers. 10
1, 5, 40, 385, 4095, 46376, 548340, 6690585, 83615350, 1064887395, 13770292256, 180320238280, 2386316821325, 31864803599700, 428798445360120, 5809228810425801, 79168272296871450, 1084567603590147950 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The generalized Catalan numbers C(k,n):= binomial(k*n+1,n)/(k*n+1) become for negative k=-|k|, with |k|>=2, ((-1)^(n-1))*binomial((|k|+1)*n-2,n)/(|k|*n-1), n>=0.

The family c(k,n):=binomial((k+1)*n-2,n)/(k*n-1), n>=1, has the members A006013, A006632, A118971 for k=2,3,4, respectively (but the offset there is 0).

The members of the C(k,n) family for positive k are: A000012 (powers of 1), A000108, A001764,A002293, A002294, A002295, A002296, A007556, A062994 for k=2..9.

REFERENCES

K. Kobayashi, H. Morita and M. Hoshi, Coding of ordered trees, Proceedings, IEEE International Symposium on Information Theory, ISIT 2000, Sorrento, Italy, Jun 25 2000.

LINKS

Table of n, a(n) for n=1..18.

FORMULA

a(n) = binomial((k+1)*n-2,n)/(k*n-1), with k=5.

G.f.: inverse series of y*(1-y)^5.

a(n) = (5/6)*binomial(6*n,n)/(6*n-1). [Bruno Berselli, Jan 17 2014]

CROSSREFS

Sequence in context: A219560 A271957 A220673 * A124555 A152601 A079158

Adjacent sequences:  A130561 A130562 A130563 * A130565 A130566 A130567

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang Jul 13 2007

STATUS

approved

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Last modified May 22 05:03 EDT 2019. Contains 323473 sequences. (Running on oeis4.)