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Search: id:A064325
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| A064325 |
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Generalized Catalan numbers C(-3; n). |
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+0
6
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| 1, 1, -2, 13, -98, 826, -7448, 70309, -686090, 6865150, -70057772, 726325810, -7628741204, 81002393668, -868066319108, 9376806129493, -101988620430938, 1116026661667318, -12277755319108748, 135715825209716038
(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)*((-3)^m)/n, m=0..n-1) = ((1/4)^n)*(1+3*sum(C(k)*(-3*4)^k, k=0..n-1)), n >= 1, a(0) := 1; with C(n)=A000108(n) (Catalan).
G.f.: (1+3*x*c(-3*x)/4)/(1-x/4) = 1/(1-x*c(-3*x)) with c(x) g.f. of Catalan numbers A000108.
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CROSSREFS
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Sequence in context: A104255 A118352 A074614 this_sequence A123619 A030519 A141116
Adjacent sequences: A064322 A064323 A064324 this_sequence A064326 A064327 A064328
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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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