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Search: id:A064343
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| A064343 |
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Generalized Catalan numbers C(5,5; n). |
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+0
2
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| 1, 1, 10, 325, 16750, 1056250, 74237500, 5580578125, 439118593750, 35714849218750, 2978473867187500, 253316015488281250, 21887247402929687500, 1915840314586914062500, 169529844641289062500000
(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)= ((25^(n-1))/(n-1))*sum((m+1)*(m+2)*binomial(2*(n-2)-m, n-2-m)*((1/5)^(m+1)), m=0..n-2), n >= 2, a(0) := 1=: a(1).
G.f.:(1-9*x*c(25*x))/(1-5*x*c(25*x))^2 = c(25*x)*(9+16*c(25*x))/(1+4*c(25*x))^2 = (9*c(25*x)*(5*x)^2+8*(2+7*x))/(4+5*x)^2 with c(x)= A(x) g.f. of Catalan numbers A000108.
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CROSSREFS
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A064342.
Sequence in context: A119297 A048345 A164055 this_sequence A127823 A113082 A046747
Adjacent sequences: A064340 A064341 A064342 this_sequence A064344 A064345 A064346
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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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