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Search: id:A130564
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| A130564 |
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Member k=5 of a family of generalized Catalan numbers. |
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+0
3
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| 1, 5, 40, 385, 4095, 46376, 548340, 6690585, 83615350, 1064887395, 13770292256, 180320238280, 2386316821325, 31864803599700, 428798445360120, 5809228810425801, 79168272296871450, 1084567603590147950
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
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REFERENCES
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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.
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FORMULA
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a(n)=binomial((k+1)*n-2,n)/(k*n-1), with k=5.
G.f.: inverse series of y*(1-y)^5.
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CROSSREFS
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Adjacent sequences: A130561 A130562 A130563 this_sequence A130565 A130566 A130567
Sequence in context: A052798 A137973 A052788 this_sequence A124555 A079158 A061633
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jul 13 2007
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