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A064327
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Generalized Catalan numbers C(-5; n).
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3
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1, 1, -4, 41, -514, 7206, -108174, 1700721, -27646234, 460887086, -7836596944, 135380098426, -2369445113804, 41925242220616, -748729419265314, 13478117036893281, -244306305241572474, 4455242518055441046
(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)*((-5)^m)/n, m=0..n-1) = ((1/6)^n)*(1+5*sum(C(k)*(-5*6)^k, k=0..n-1)), n >= 1, a(0) := 1; with C(n)=A000108(n) (Catalan).
G.f.: (1+5*x*c(-5*x)/6)/(1-x/6) = 1/(1-x*c(-5*x)) with c(x) g.f. of Catalan numbers A000108.
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CROSSREFS
| Sequence in context: A118450 A024383 A110041 * A134277 A085340 A001908
Adjacent sequences: A064324 A064325 A064326 * A064328 A064329 A064330
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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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