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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 Seiichi Manyama, Table of n, a(n) for n = 3..225 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 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, A211374. Sequence in context: A059420 A129906 A125722 * A201724 A006410 A159874 Adjacent sequences:  A226728 A226729 A226730 * A226732 A226733 A226734 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Jun 15 2013 STATUS approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)