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Search: id:A064333
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| A064333 |
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Generalized Catalan numbers C(-11; n). |
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+0
2
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| 1, 1, -10, 221, -6082, 187386, -6184848, 213843477, -7645509706, 280351640702, -10485617230780, 398467433529298, -15341431926699284, 597149747213056324, -23459916801814723548, 929028306450848244741, -37045540042729366580442
(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)*((-11)^m)/n, m=0..n-1) = ((1/12)^n)*(1+11*sum(C(k)*(-11*12)^k, k=0..n-1)), n >= 1, a(0) := 1; with C(n)=A000108(n) (Catalan).
G.f.: (1+11*x*c(-11*x)/12)/(1-x/12) = 1/(1-x*c(-11*x)) with c(x) g.f. of Catalan numbers A000108.
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CROSSREFS
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Adjacent sequences: A064330 A064331 A064332 this_sequence A064334 A064335 A064336
Sequence in context: A024292 A094420 A053131 this_sequence A052789 A092254 A004702
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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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