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A064325
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Generalized Catalan numbers C(-3; n).
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5
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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; 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)*((-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
| Sequence in context: A118352 A074614 A184019 * A123619 A030519 A141116
Adjacent sequences: A064322 A064323 A064324 * A064326 A064327 A064328
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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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