A004529 Ratios of successive terms are 1,1,1,2,3,3,3,4,5,5,5,6,...

1, 1, 1, 1, 2, 6, 18, 54, 216, 1080, 5400, 27000, 162000, 1134000, 7938000, 55566000, 444528000, 4000752000, 36006768000, 324060912000, 3240609120000, 35646700320000, 392113703520000, 4313250738720000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..506

Programs

Maple

seq(seq(16^k * k! * GAMMA(k+1/2)^3*(2*k+1)^j/GAMMA(1/2)^3,j=0..3),k=0..10); # Robert Israel, Jun 19 2018

Formula

a(n) = Product_{j=0..n-1} (A180969(2,j+1) + A180969(2,j) + 1) = a(n-1) * (A180969(2,n-1) + A180969(2,n-2) + 1). - Adriano Caroli, Nov 27 2010

a(4*k+j) = 16^k * k! * Gamma(k+1/2)^3*(2*k+1)^j/Gamma(1/2)^3 for 0 <= j <= 3. - Robert Israel, Jun 19 2018