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A064093 Generalized Catalan numbers C(10; n). 2
1, 1, 11, 221, 5531, 154941, 4649451, 146150061, 4750427771, 158361063581, 5384626548491, 186023930383501, 6511108452179611, 230400987949757821, 8228844334672249131, 296245683962814194541, 10739133812893020645051 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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).

LINKS

Table of n, a(n) for n=0..16.

FORMULA

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) } . - Philippe Deléham, Jan 19 2004

CROSSREFS

A064092 (C(9, n)).

Sequence in context: A035012 A179339 A055411 * A087402 A048377 A192686

Adjacent sequences:  A064090 A064091 A064092 * A064094 A064095 A064096

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Sep 13 2001

STATUS

approved

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Last modified February 25 00:39 EST 2018. Contains 299630 sequences. (Running on oeis4.)