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A064341
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Generalized Catalan numbers C(3,3; n).
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1
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1, 1, 6, 81, 1566, 36126, 921456, 25055001, 711951606, 20891575566, 628237506276, 19259213633226, 599654171202156, 18911332670183856, 602840023457208516, 19392890824608619401, 628769286622411762086
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OFFSET
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0,3
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COMMENTS
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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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LINKS
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Table of n, a(n) for n=0..16.
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FORMULA
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a(n)= ((9^(n-1))/(n-1))*sum((m+1)*(m+2)*binomial(2*(n-2)-m, n-2-m)*((1/3)^(m+1)), m=0..n-2), n >= 2, a(0) := 1=: a(1).
G.f.:(1-5*x*c(9*x))/(1-3*x*c(9*x))^2 = c(9*x)*(5+4*c(9*x))/(1+2*c(9*x))^2 = (5*c(9*x)*(3*x)^2+4*(1+4*x))/(2+3*x)^2 with c(x)= A(x) g.f. of Catalan numbers A000108.
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CROSSREFS
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A064340.
Sequence in context: A052348 A196909 A197076 * A052756 A193265 A138457
Adjacent sequences: A064338 A064339 A064340 * A064342 A064343 A064344
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang, Oct 12 2001
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STATUS
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approved
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