A064346 Generalized Catalan numbers C(8,8; n).

1, 1, 16, 1216, 157696, 25317376, 4543676416, 873117515776, 175715349692416, 36562356662173696, 7802094251017240576, 1698089607837490610176, 375493988522687218057216, 84121868091432283370684416

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.

J. Abate, W. Whitt, Brownian Motion and the Generalized Catalan Numbers, J. Int. Seq. 14 (2011) # 11.2.6, corollary 6.

Formula

a(n)= ((8^(2*(n-1)))/(n-1))*sum((m+1)*(m+2)*binomial(2*(n-2)-m, n-2-m)*((1/8)^(m+1)), m=0..n-2), n >= 2, a(0) := 1=: a(1).

G.f.:(1-15*x*c(64*x))/(1-8*x*c(64*x))^2 = c(64*x)*(15+49*c(64*x))/(1+7*c(64*x))^2 = (15*c(64*x)*(8*x)^2+7*(7+23*x))/(7+8*x)^2 with c(x)= A(x) g.f. of Catalan numbers A000108.

7*(-n+1)*a(n) +8*(223*n-560)*a(n-1) +1024*(2*n-3)*a(n-2)=0. - R. J. Mathar, Aug 09 2017

Crossrefs

A064345.

Sequence in context: A373453 A160131 A206691 * A222888 A113104 A227602

Adjacent sequences: A064343 A064344 A064345 * A064347 A064348 A064349

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 12 2001

Status

approved