central binomial coefficients modulo (was catalans modulo)

[Antti Karttunen]

"Meeussen Wouter (bkarnd)" wrote:

> dear Antti,
>
> check again,
> it's the Catalans all right, but with offset 1 (instead of the usual 0)

How do you get that? I interpret the . in Claude's line

> Let be the Catalan's numbers defined by
>
> c(1)=1, (n+1).c(n+1)=2.(2n-1).c(n).

to mean multiplication, so I get this recursive Maple
formula:
c := n -> `if`((1 = n),1,(2*((2*n)-1)*c(n-1))/n);

and computing, we get:
[seq(c(j),j=1..20)];
[1, 3, 10, 35, 126, 462, 1716, 6435, 24310, 92378, 352716, 1352078,

    5200300, 20058300, 77558760, 300540195, 1166803110, 4537567650,

    17672631900, 68923264410]


????

-- Antti