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Search: id:A130565
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| A130565 |
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Member k=6 of a family of generalized Catalan numbers. |
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+0
1
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| 1, 6, 57, 650, 8184, 109668, 1533939, 22137570, 327203085, 4928006512, 75357373305, 1166880131820, 18259838103852, 288308609783760, 4587430875645660, 73484989079268690, 1184104656043939071
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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.
For the members of the family C(k,n), k=2..9, see A130564.
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) and A130564 for k=5.
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FORMULA
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a(n)=binomial((k+1)*n-2,n)/(k*n-1), with k=6.
G.f.: inverse series of y*(1-y)^6.
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CROSSREFS
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Cf. k=5 member A130564.
Sequence in context: A124546 A095900 A138414 this_sequence A124556 A060435 A141372
Adjacent sequences: A130562 A130563 A130564 this_sequence A130566 A130567 A130568
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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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