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Search: id:A064328
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| A064328 |
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Generalized Catalan numbers C(-6; n). |
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+0
3
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| 1, 1, -5, 61, -917, 15421, -277733, 5239117, -102188021, 2044131037, -41706059525, 864547613293, -18157111255829, 385517710342909, -8261602828082213, 178459989617336461, -3881680470161846837
(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)*((-6)^m)/n, m=0..n-1) = ((1/7)^n)*(1+6*sum(C(k)*(-6*7)^k, k=0..n-1)), n >= 1, a(0) := 1; with C(n)=A000108(n) (Catalan).
G.f.: (1+6*x*c(-6*x)/7)/(1-x/7) = 1/(1-x*c(-6*x)) with c(x) g.f. of Catalan numbers A000108.
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CROSSREFS
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Sequence in context: A060060 A000363 A099666 this_sequence A012060 A012167 A162167
Adjacent sequences: A064325 A064326 A064327 this_sequence A064329 A064330 A064331
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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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