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Search: id:A064092
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| A064092 |
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Generalized Catalan numbers C(9; n). |
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+0
6
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| 1, 1, 10, 181, 4078, 102826, 2777212, 78571837, 2298558934, 68964092542, 2110472708140, 65620725560578, 2067160250751436, 65833929303952564, 2116166898185821792, 68565914052628406221, 2237022199842087256678
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n+1)= Y_{n}(n+1)= Z_{n}, n >= 0, in the Derrida et al. 1992 reference (see A064094) for alpha=9, beta =1 (or alpha=1, beta=9).
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FORMULA
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G.f.: (1+9*x*c(9*x)/8)/(1+x/8) = 1/(1-x*c(9*x)) with c(x) g.f. of Catalan numbers A000108.
a(n)= sum((n-m)*binomial(n-1+m, m)*(9^m)/n, m=0..n-1) = ((-1/8)^n)*(1-9*sum(C(k)*(-72)^k, k=0..n-1)), n >= 1, a(0) := 1; with C(n)=A000108(n) (Catalan).
a(n) = Sum{ k= 0...n, A059365(n, k)*9^(n-k) } . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 19 2004
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff(serreverse((x-8*x^2)/(1+x)^2+O(x^(n+1))), n)) (from R. Stephan)
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CROSSREFS
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A064091 (C(8, n)).
Sequence in context: A030048 A054918 A095807 this_sequence A121973 A006409 A056174
Adjacent sequences: A064089 A064090 A064091 this_sequence A064093 A064094 A064095
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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), Sep 13 2001
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