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Search: id:A064342
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| A064342 |
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Generalized Catalan numbers C(4,4; n). |
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+0
2
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| 1, 1, 8, 176, 5888, 238848, 10770432, 518909952, 26156466176, 1362414338048, 72751723839488, 3961437637574656, 219123329636761600, 12278352550322765824, 695492547259800748032, 39759203500044029263872
(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)= ((16^(n-1))/(n-1))*sum((m+1)*(m+2)*binomial(2*(n-2)-m, n-2-m)*((1/4)^(m+1)), m=0..n-2), n >= 2, a(0) := 1=: a(1).
G.f.:(1-7*x*c(16*x))/(1-4*x*c(16*x))^2 = c(16*x)*(7+9*c(16*x))/(1+3*c(16*x))^2 = (7*c(16*x)*(4*x)^2+3*(3+11*x))/(3+4*x)^2 with c(x)= A(x) g.f. of Catalan numbers A000108.
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CROSSREFS
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A064341.
Sequence in context: A067637 A024109 A027464 this_sequence A099175 A000839 A001596
Adjacent sequences: A064339 A064340 A064341 this_sequence A064343 A064344 A064345
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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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