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 A190903 Product_{k in M_n} k, M_n = {k | 1 <= k <= 3n and k mod 3 = n mod 3}. 1

%I

%S 1,1,10,162,280,12320,524880,1106560,96342400,7142567040,17041024000,

%T 2324549427200,254561089305600,664565853952000,126757680265216000,

%U 18763697892715776000,52580450364682240000,13106744139423334400000

%N Product_{k in M_n} k, M_n = {k | 1 <= k <= 3n and k mod 3 = n mod 3}.

%C For n > 0:

%C a(3*n) = A032031(3*n) = 3^(3*n) * Gamma(3*n + 1).

%C a(3*n-1) = A008544(3*n-1) = 3^(3*n-1) * Gamma(3*n - 1/3) / Gamma(2/3).

%C a(3*n+1) = A007559(3*n+1) = 3^(3*n+3/2) * Gamma(3*n + 4/3) * Gamma(2/3) / (2*Pi).

%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/Multifactorials">Multifactorials</a>

%F From _Johannes W. Meijer_, Jul 04 2011: (Start)

%F a(3*n+3)/(a(3*n)*a(3)) = A006566(n+1); Dodecahedral numbers

%F a(3*n+4)/a(3*n+1) = A136214(3*n+4, 3*n+1)

%F a(3*n+5)/a(3*n+2) = A112333(3*n+5, 3*n+2) (End)

%p A190903 := proc(n) local k; mul(k, k = select(k-> k mod 3 = n mod 3, [\$1 .. 3*n])) end: seq(A190903(n), n=0..17);

%Y Cf. A190901.

%K nonn

%O 0,3

%A _Peter Luschny_, Jul 03 2011

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