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Search: id:A064090
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| A064090 |
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Generalized Catalan numbers C(7; n). |
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+0
5
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| 1, 1, 8, 113, 1982, 38886, 817062, 17981769, 409186310, 9549411950, 227307541448, 5497312072330, 134696099554276, 3336563455537768, 83419226227330722, 2102274863070771033, 53347639317495439302
(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=7, beta =1 (or alpha=1, beta=7).
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FORMULA
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G.f.: (1+7*x*c(7*x)/6)/(1+x/6) = 1/(1-x*c(7*x)) with c(x) g.f. of Catalan numbers A000108.
a(n)= sum((n-m)*binomial(n-1+m, m)*(7^m)/n, m=0..n-1) = ((-1/6)^n)*(1-7*sum(C(k)*(-42)^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)*7^(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-6*x^2)/(1+x)^2+O(x^(n+1))), n)) (from R. Stephan)
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CROSSREFS
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A064089 (C(6, n)).
Sequence in context: A034689 A010041 A099703 this_sequence A072402 A092084 A099715
Adjacent sequences: A064087 A064088 A064089 this_sequence A064091 A064092 A064093
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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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