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A064326
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Generalized Catalan numbers C(-4; n).
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2
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1, 1, -3, 25, -251, 2817, -33843, 425769, -5537835, 73865617, -1004862179, 13888533561, -194475377243, 2752994728225, -39333541106835, 566464908534345, -8214515461250955, 119845125957958065, -1757855400878129475
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| See triangle A064334 with columns m built from C(-m; n), m >= 0, also for Derrida et al. references.
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FORMULA
| a(n)= sum((n-m)*binomial(n-1+m, m)*((-4)^m)/n, m=0..n-1) = ((1/5)^n)*(1+4*sum(C(k)*(-4*5)^k, k=0..n-1)), n >= 1, a(0) := 1; with C(n)=A000108(n) (Catalan).
G.f.: (1+4*x*c(-4*x)/5)/(1-x/5) = 1/(1-x*c(-4*x)) with c(x) g.f. of Catalan numbers A000108.
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CROSSREFS
| Sequence in context: A171640 A099913 A086655 * A006091 A009042 A080896
Adjacent sequences: A064323 A064324 A064325 * A064327 A064328 A064329
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KEYWORD
| sign,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Sep 21 2001
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