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 A130565 Member k=6 of a family of generalized Catalan numbers. 8
 1, 6, 57, 650, 8184, 109668, 1533939, 22137570, 327203085, 4928006512, 75357373305, 1166880131820, 18259838103852, 288308609783760, 4587430875645660, 73484989079268690, 1184104656043939071 (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. 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. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..806 FORMULA a(n) = binomial((k+1)*n-2,n)/(k*n-1), with k=6. G.f.: inverse series of y*(1-y)^6. a(n) = (6/7)*binomial(7*n,n)/(7*n-1). [Bruno Berselli, Jan 17 2014] MATHEMATICA Table[Binomial[7n-2, n]/(6n-1), {n, 20}] (* Harvey P. Dale, Feb 25 2013 *) CROSSREFS Cf. k=5 member A130564. Sequence in context: A246235 A213105 A138414 * A124556 A207412 A324447 Adjacent sequences:  A130562 A130563 A130564 * A130566 A130567 A130568 KEYWORD nonn,easy AUTHOR Wolfdieter Lang Jul 13 2007 STATUS approved

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Last modified May 19 03:16 EDT 2019. Contains 323377 sequences. (Running on oeis4.)