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Search: id:A064347
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| A064347 |
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Generalized Catalan numbers C(9,9; n). |
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+0
2
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| 1, 1, 18, 1701, 278478, 56542698, 12838905972, 3121895416077, 795077021525526, 209364566760439038, 56540432581528153788, 15573764062988183490786, 4358381303784085630372620, 1235729432868053981694246324
(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)= ((9^(2*(n-1)))/(n-1))*sum((m+1)*(m+2)*binomial(2*(n-2)-m, n-2-m)*((1/9)^(m+1)), m=0..n-2), n >= 2, a(0) := 1=: a(1).
G.f.:(1-17*x*c(81*x))/(1-9*x*c(81*x))^2 = c(81*x)*(17+64*c(81*x))/(1+8*c(81*x))^2 = (17*c(81*x)*(9*x)^2+16*(4+13*x))/(8+9*x)^2 with c(x)= A(x) g.f. of Catalan numbers A000108.
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CROSSREFS
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A064346.
Sequence in context: A003030 A086366 A086193 this_sequence A067303 A055740 A072477
Adjacent sequences: A064344 A064345 A064346 this_sequence A064348 A064349 A064350
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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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