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Search: id:A064330
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| A064330 |
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Generalized Catalan numbers C(-8; n). |
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+0
2
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| 1, 1, -7, 113, -2263, 50721, -1217703, 30622929, -796311415, 21237226625, -577699502407, 15966537989425, -447086291268119, 12656524451911393, -361628025405250023, 10415207118205622673, -302049007052246016183
(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 A064334 with columns m built from C(-m; n), m >= 0, also for Derrida et al. references.
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FORMULA
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a(n)= sum((n-m)*binomial(n-1+m, m)*((-8)^m)/n, m=0..n-1) = ((1/9)^n)*(1+8*sum(C(k)*(-8*9)^k, k=0..n-1)), n >= 1, a(0) := 1; with C(n)=A000108(n) (Catalan).
G.f.: (1+8*x*c(-8*x)/9)/(1-x/9) = 1/(1-x*c(-8*x)) with c(x) g.f. of Catalan numbers A000108.
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CROSSREFS
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Sequence in context: A081531 A142537 A084974 this_sequence A086788 A127877 A082487
Adjacent sequences: A064327 A064328 A064329 this_sequence A064331 A064332 A064333
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KEYWORD
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sign,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Sep 21 2001
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