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Search: id:A064089
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| A064089 |
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Generalized Catalan numbers C(6; n). |
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+0
3
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| 1, 1, 7, 85, 1279, 21517, 387607, 7312789, 142648495, 2853691357, 58226571271, 1207062556261, 25351452769567, 538285926177325, 11535690316148215, 249189167966657845, 5420206822556721295
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n+1)= Y_{n}(n+1)= Z_{n}, n >= 0, in the Derrida et al. 1992 reference (see A064094) for alpha=6, beta =1 (or alpha=1, beta=6).
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FORMULA
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G.f.: (1+6*x*c(6*x)/5)/(1+x/5) = 1/(1-x*c(6*x)) with c(x) g.f. of Catalan numbers A000108.
a(n)= sum((n-m)*binomial(n-1+m, m)*(6^m)/n, m=0..n-1) = ((-1/5)^n)*(1-6*sum(C(k)*(-30)^k, k=0..n-1)), n >= 1, a(0) := 1; with C(n)=A000108(n) (Catalan).
a(n) = Sum{ k= 0...n, A059365(n, k)*6^(n-k) } . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 19 2004
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff(serreverse((x-5*x^2)/(1+x)^2+O(x^(n+1))), n)) (from R. Stephan)
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CROSSREFS
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A064088 (C(5, n)).
Sequence in context: A027531 A126344 A026001 this_sequence A049412 A056547 A121020
Adjacent sequences: A064086 A064087 A064088 this_sequence A064090 A064091 A064092
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Sep 13 2001
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