|
| |
|
|
A064345
|
|
Generalized Catalan numbers C(7,7; n).
|
|
1
| |
|
|
1, 1, 14, 833, 83006, 10213854, 1404124008, 206635997673, 31844571309110, 5073749573133710, 829012595472718580, 138151786440502006186, 23390450962161609522028, 4012173837912126230070832
(list; graph; refs; listen; history; 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.
|
|
|
FORMULA
| a(n)= ((7^(2*(n-1)))/(n-1))*sum((m+1)*(m+2)*binomial(2*(n-2)-m, n-2-m)*((1/7)^(m+1)), m=0..n-2), n >= 2, a(0) := 1=: a(1).
G.f.:(1-13*x*c(49*x))/(1-7*x*c(49*x))^2 = c(49*x)*(13+36*c(49*x))/(1+6*c(49*x))^2 = (13*c(49*x)*(7*x)^2+12*(3+10*x))/(6+7*x)^2 with c(x)= A(x) g.f. of Catalan numbers A000108.
|
|
|
CROSSREFS
| A064344.
Sequence in context: A050983 A183576 A002429 * A159871 A115458 A199651
Adjacent sequences: A064342 A064343 A064344 * A064346 A064347 A064348
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 12 2001
|
| |
|
|
