A113550 a(n) = product of n successive numbers up to n, if n is odd a(n) = n*(n-1)*.. = n!, if n is even a(n) = n(n+1)(n+2)... 'n' terms.
1, 6, 6, 840, 120, 332640, 5040, 259459200, 362880, 335221286400, 39916800, 647647525324800, 6227020800, 1748648318376960000, 1307674368000, 6288139352883548160000, 355687428096000, 29051203810321992499200000, 121645100408832000, 167683548393178540705382400000
Offset: 1
Examples
a(3) = 3*2*1 = 6. a(4) = 4*5*6*7 = 840.
Links
- G. C. Greubel, Table of n, a(n) for n = 1..350
Programs
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Mathematica
n = 1; anfunc[n_] := (If [EvenQ[n], {an = n, Do[an = an*(n + i), {i, n - 1}]}, an = n! ]; an); Table[anfunc[n], {n, 1, 20}] (* Elizabeth A. Blickley (Elizabeth.Blickley(AT)gmail.com), Mar 10 2006 *)
Formula
a(2n-1) = (2n-1)!, a(2n) = (4n-1)!/(2n-1)!.
a(2n-1)*a(2n) = (4n-1)!.
Sum_{n>=1} 1/a(n) = sinh(1) + (sqrt(Pi)/2) * (exp(1/4) * erf(1/2) - exp(-1/4) * erfi(1/2)). - Amiram Eldar, Aug 15 2025
Extensions
More terms from Elizabeth A. Blickley (Elizabeth.Blickley(AT)gmail.com), Mar 10 2006