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Search: id:A064340
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| A064340 |
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Generalized Catalan numbers C(2,2; n). |
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+0
11
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| 1, 1, 4, 28, 256, 2704, 31168, 380608, 4840960, 63458560, 851399680, 11635096576, 161396604928, 2266669453312, 32166082822144, 460531091685376, 6644185553305600, 96498260064403456, 1409750653282287616
(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)= ((4^(n-1))/(n-1))*sum((m+1)*(m+2)*binomial(2*(n-2)-m, n-2-m)*((1/2)^(m+1)), m=0..n-2), n >= 2, a(0) := 1=: a(1).
G.f.:(1-3*x*c(4*x))/(1-2*x*c(4*x))^2 = c(4*x)*(3+c(4*x))/(1+c(4*x))^2 = (1+5*x+3*c(4*x)*(2*x)^2)/(1+2*x)^2 with c(x)= A(x) g.f. of Catalan numbers A000108.
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CROSSREFS
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A000108 (Catalan as C(1, 1, n)).
Sequence in context: A151830 A112113 A103211 this_sequence A002895 A141004 A152410
Adjacent sequences: A064337 A064338 A064339 this_sequence A064341 A064342 A064343
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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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