|
| |
|
|
A064344
|
|
Generalized Catalan numbers C(6,6; n).
|
|
1
|
|
|
|
1, 1, 12, 540, 39744, 3598992, 363776832, 39348690624, 4456429954560, 521760612125952, 62642882007530496, 7670452375558388736, 954216689151845302272, 120261048050627578368000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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..13.
|
|
|
FORMULA
|
a(n)= ((6^(2*(n-1)))/(n-1))*sum((m+1)*(m+2)*binomial(2*(n-2)-m, n-2-m)*((1/6)^(m+1)), m=0..n-2), n >= 2, a(0) := 1=: a(1).
G.f.:(1-11*x*c(36*x))/(1-6*x*c(36*x))^2 = c(36*x)*(11+25*c(36*x))/(1+5*c(36*x))^2 = (11*c(36*x)*(6*x)^2+5*(5+17*x))/(5+6*x)^2 with c(x)= A(x) g.f. of Catalan numbers A000108.
|
|
|
CROSSREFS
|
A064343.
Sequence in context: A202079 A067733 A184423 * A163046 A193381 A224539
Adjacent sequences: A064341 A064342 A064343 * A064345 A064346 A064347
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Wolfdieter Lang, Oct 12 2001
|
|
|
STATUS
|
approved
|
| |
|
|
