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A064091
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Generalized Catalan numbers C(8; n).
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3
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1, 1, 9, 145, 2905, 65121, 1563561, 39322929, 1022586105, 27272680705, 741894295369, 20504949587409, 574176887116441, 16254518495907745, 464436319229036265, 13376293681432402545, 387925710986712480825
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n+1)= Y_{n}(n+1)= Z_{n}, n >= 0, in the Derrida et al. 1992 reference (see A064094) for alpha=8, beta =1 (or alpha=1, beta=8).
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FORMULA
| G.f.: (1+8*x*c(8*x)/7)/(1+x/7) = 1/(1-x*c(8*x)) with c(x) g.f. of Catalan numbers A000108.
a(n)=sum((n-m)*binomial(n-1+m, m)*(8^m)/n, m=0..n-1) = ((-1/7)^n)*(1-8*sum(C(k)*(-56)^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)*8^(n-k) } . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 19 2004
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PROG
| (PARI) a(n)=if(n<0, 0, polcoeff(serreverse((x-7*x^2)/(1+x)^2+O(x^(n+1))), n)) (from R. Stephan)
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CROSSREFS
| A064090 (C(7, n)).
Sequence in context: A094594 A173213 A046529 * A132060 A178185 A006691
Adjacent sequences: A064088 A064089 A064090 * A064092 A064093 A064094
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Sep 13 2001
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