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Search: id:A064346
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| A064346 |
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Generalized Catalan numbers C(8,8; n). |
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+0
2
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| 1, 1, 16, 1216, 157696, 25317376, 4543676416, 873117515776, 175715349692416, 36562356662173696, 7802094251017240576, 1698089607837490610176, 375493988522687218057216, 84121868091432283370684416
(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)= ((8^(2*(n-1)))/(n-1))*sum((m+1)*(m+2)*binomial(2*(n-2)-m, n-2-m)*((1/8)^(m+1)), m=0..n-2), n >= 2, a(0) := 1=: a(1).
G.f.:(1-15*x*c(64*x))/(1-8*x*c(64*x))^2 = c(64*x)*(15+49*c(64*x))/(1+7*c(64*x))^2 = (15*c(64*x)*(8*x)^2+7*(7+23*x))/(7+8*x)^2 with c(x)= A(x) g.f. of Catalan numbers A000108.
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CROSSREFS
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A064345.
Sequence in context: A029701 A053903 A102807 this_sequence A113104 A000490 A027648
Adjacent sequences: A064343 A064344 A064345 this_sequence A064347 A064348 A064349
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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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