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Search: id:A064344
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| A064344 |
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Generalized Catalan numbers C(6,6; n). |
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+0
2
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| 1, 1, 12, 540, 39744, 3598992, 363776832, 39348690624, 4456429954560, 521760612125952, 62642882007530496, 7670452375558388736, 954216689151845302272, 120261048050627578368000
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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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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.
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CROSSREFS
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A064343.
Adjacent sequences: A064341 A064342 A064343 this_sequence A064345 A064346 A064347
Sequence in context: A012466 A004801 A067733 this_sequence A133415 A042111 A013587
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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), Oct 12 2001
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