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Search: id:A064332
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| A064332 |
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Generalized Catalan numbers C(-10; n). |
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+0
2
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| 1, 1, -9, 181, -4529, 126861, -3806649, 119653941, -3889122369, 129646443421, -4408213959689, 152290162367301, -5330337257966609, 188617242067457581, -6736489341630231129, 242518500968942706261, -8791448318093732481249
(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)*((-10)^m)/n, m=0..n-1) = ((1/11)^n)*(1+10*sum(C(k)*(-10*11)^k, k=0..n-1)), n >= 1, a(0) := 1; with C(n)=A000108(n) (Catalan).
G.f.: (1+10*x*c(-10*x)/11)/(1-x/11) = 1/(1-x*c(-10*x)) with c(x) g.f. of Catalan numbers A000108.
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CROSSREFS
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Sequence in context: A009009 A034221 A034240 this_sequence A078101 A133556 A124008
Adjacent sequences: A064329 A064330 A064331 this_sequence A064333 A064334 A064335
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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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