A226731 a(n) = (2n - 1)!/(2n).

20, 630, 36288, 3326400, 444787200, 81729648000, 19760412672000, 6082255020441600, 2322315553259520000, 1077167364120207360000, 596585001666576384000000, 388888194657798291456000000

Offset

3,1

Comments

For n < 3, the formula does not produce an integer.

The ratio of the product of the partition parts of 2n into exactly two parts to the sum of the partition parts of 2n into exactly two parts. For example, a(3) = 20, and 2*3 = 6 has 3 partitions into exactly two parts: (5,1), (4,2), (3,3). Forming the ratio of product to sum (of parts), we have (5*1*4*2*3*3)/(5+1+4+2+3+3) = 360/18 = 20. - Wesley Ivan Hurt, Jun 24 2013

Links

Seiichi Manyama, Table of n, a(n) for n = 3..225

Index entries for sequences related to partitions.

Formula

a(n) = A009445(n-1)/A005843(n) = A002674(n)/A001105(n). - Wesley Ivan Hurt, Jun 24 2013

a(n) ~ sqrt(Pi)*2^(2*n-1)*n^(2*n-3/2)/exp(2*n). - Ilya Gutkovskiy, Nov 01 2016

From Amiram Eldar, Mar 10 2022: (Start)

Sum_{n>=3} 1/a(n) = e - 8/3.

Sum_{n>=3} (-1)^(n+1)/a(n) = cos(1) + sin(1) - 4/3. (End)

Example

a(3) = (2*3 - 1)!/(2*3) = 5!/6 = 120/6 = 20.

Maple

seq((2*k-1)!/(2*k), k=1..20); # Wesley Ivan Hurt, Jun 24 2013

Mathematica

Table[(2n-1)!/(2n), {n, 3, 20}] (* Harvey P. Dale, Jun 19 2013 *)

Prog

(PARI) a(n) = (2*n-1)!/(2*n); \\ Michel Marcus, Nov 01 2016

Crossrefs

Cf. A001105, A002674, A005843, A009445, A093353, A143623, A211374.

Sequence in context: A129906 A125722 A336412 * A201724 A006410 A159874

Adjacent sequences: A226728 A226729 A226730 * A226732 A226733 A226734

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jun 15 2013

Status

approved