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Search: id:A064093
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| A064093 |
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Generalized Catalan numbers C(10; n). |
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+0
3
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| 1, 1, 11, 221, 5531, 154941, 4649451, 146150061, 4750427771, 158361063581, 5384626548491, 186023930383501, 6511108452179611, 230400987949757821, 8228844334672249131, 296245683962814194541, 10739133812893020645051
(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=10, beta =1 (or alpha=1, beta=10).
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FORMULA
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G.f.: (1+10*x*c(10*x)/9)/(1+x/9) = 1/(1-x*c(10*x)) with c(x) g.f. of Catalan numbers A000108.
a(n)= sum((n-m)*binomial(n-1+m, m)*(10^m)/n, m=0..n-1) = ((-1/9)^n)*(1-10*sum(C(k)*(-90)^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)*10^(n-k) } . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 19 2004
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CROSSREFS
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A064092 (C(9, n)).
Sequence in context: A160074 A035012 A055411 this_sequence A087402 A048377 A103611
Adjacent sequences: A064090 A064091 A064092 this_sequence A064094 A064095 A064096
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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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