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Search: id:A064331
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| A064331 |
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Generalized Catalan numbers C(-9; n). |
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+0
4
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| 1, 1, -8, 145, -3266, 82342, -2223818, 62912809, -1840413050, 55217088622, -1689752866904, 52538652432586, -1655036407913948, 52708355827445800, -1694246075896308110, 54894923324331676345, -1790984858946499478330
(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)*((-9)^m)/n, m=0..n-1) = ((1/10)^n)*(1+9*sum(C(k)*(-9*10)^k, k=0..n-1)), n >= 1, a(0) := 1; with C(n)=A000108(n) (Catalan).
G.f.: (1+9*x*c(-9*x)/10)/(1-x/10) = 1/(1-x*c(-9*x)) with c(x) g.f. of Catalan numbers A000108.
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CROSSREFS
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Sequence in context: A071305 A105046 A123812 this_sequence A116876 A075351 A003491
Adjacent sequences: A064328 A064329 A064330 this_sequence A064332 A064333 A064334
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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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