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A064346
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Generalized Catalan numbers C(8,8; n).
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1
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1, 1, 16, 1216, 157696, 25317376, 4543676416, 873117515776, 175715349692416, 36562356662173696, 7802094251017240576, 1698089607837490610176, 375493988522687218057216, 84121868091432283370684416
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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
| 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
| A064345.
Sequence in context: A102807 A160131 A206691 * A113104 A186856 A000490
Adjacent sequences: A064343 A064344 A064345 * A064347 A064348 A064349
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 12 2001
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