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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 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

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