A064878 Generalized Catalan numbers C(10,10; n).

1, 1, 20, 2300, 464000, 116250000, 32580600000, 9779307000000, 3074524280000000, 999451946900000000, 333207298730000000000, 113305219025110000000000, 39145823948711200000000000

Offset

0,3

Comments

See triangle A064879 with columns m built from C(m,m; n), m >= 0, also for Derrida et al. and Liggett references.

Links

Table of n, a(n) for n=0..12.

Formula

a(n)= ((10^(2*(n-1)))/(n-1))*sum((m+1)*(m+2)*binomial(2*(n-2)-m, n-2-m)*((1/10)^(m+1)), m=0..n-2), n >= 2, a(0) := 1=: a(1).

G.f.:(1-19*x*c(100*x))/(1-10*x*c(100*x))^2 = c(100*x)*(19+81*c(100*x))/(1+9*c(100*x))^2 = (19*c(100*x)*(10*x)^2+9*(9+29*x))/(9+10*x)^2 with c(x)= A(x) g.f. of Catalan numbers A000108.

Crossrefs

A064347.

Sequence in context: A195622 A305658 A329067 * A222943 A222750 A250019

Adjacent sequences: A064875 A064876 A064877 * A064879 A064880 A064881

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 12 2001

Status

approved