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A226731 a(n) = (2n - 1)!/(2n). 1
20, 630, 36288, 3326400, 444787200, 81729648000, 19760412672000, 6082255020441600, 2322315553259520000, 1077167364120207360000, 596585001666576384000000, 388888194657798291456000000 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A129906 A125722 A336412 * A201724 A006410 A159874
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jun 15 2013
STATUS
approved

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Last modified July 22 13:14 EDT 2024. Contains 374499 sequences. (Running on oeis4.)