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A064344
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Generalized Catalan numbers C(6,6; n).
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1
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1, 1, 12, 540, 39744, 3598992, 363776832, 39348690624, 4456429954560, 521760612125952, 62642882007530496, 7670452375558388736, 954216689151845302272, 120261048050627578368000
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OFFSET
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0,3
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COMMENTS
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See triangle A064879 with columns m built from C(m,m; n), m >= 0, also for Derrida et al.and Liggett references.
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LINKS
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Table of n, a(n) for n=0..13.
J. Abate, W. Whitt, Brownian Motion and the Generalized Catalan Numbers, J. Int. Seq. 14 (2011) # 11.2.6, corollary 6.
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FORMULA
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a(n)= ((6^(2*(n-1)))/(n-1))*sum((m+1)*(m+2)*binomial(2*(n-2)-m, n-2-m)*((1/6)^(m+1)), m=0..n-2), n >= 2, a(0) := 1=: a(1).
G.f.:(1-11*x*c(36*x))/(1-6*x*c(36*x))^2 = c(36*x)*(11+25*c(36*x))/(1+5*c(36*x))^2 = (11*c(36*x)*(6*x)^2+5*(5+17*x))/(5+6*x)^2 with c(x)= A(x) g.f. of Catalan numbers A000108.
5*(-n+1)*a(n) +6*(119*n-300)*a(n-1) +432*(2*n-3)*a(n-2)=0. - R. J. Mathar, Aug 09 2017
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CROSSREFS
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A064343.
Sequence in context: A353194 A285748 A184423 * A163046 A193381 A224539
Adjacent sequences: A064341 A064342 A064343 * A064345 A064346 A064347
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang, Oct 12 2001
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STATUS
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approved
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