A190901 a(n) = Product_{k in M_n} k; M_n = {k | 1 <= k <= 2n and k mod 2 = n mod 2}.

1, 1, 8, 15, 384, 945, 46080, 135135, 10321920, 34459425, 3715891200, 13749310575, 1961990553600, 7905853580625, 1428329123020800, 6190283353629375, 1371195958099968000, 6332659870762850625, 1678343852714360832000

Offset: 0

Author

Peter Luschny, Jun 23 2011

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..400
• Peter Luschny, Multifactorials

Programs

Maple

A190901 := proc(n) local k; mul(k, k = select(k-> k mod 2 = n mod 2, [$1 .. 2*n])) end: seq(A190901(n), n=0..18);

Mathematica

a[n_] := With[{m = Mod[n, 2]}, Product[If[Mod[k, 2] == m, k, 1], {k, 1, 2*n}]]; Table[a[n], {n, 0, 18}] (* Jean-François Alcover, Jan 27 2014 *)

Formula

a(2*k) = A006882(4*k) = 4^k * Gamma(2*k+1).

a(2*k+1) = A001147(2*k+1) = 4^k * Gamma(2*k+3/2) / sqrt(Pi/4).