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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
 1, 1, 10, 162, 280, 12320, 524880, 1106560, 96342400, 7142567040, 17041024000, 2324549427200, 254561089305600, 664565853952000, 126757680265216000, 18763697892715776000, 52580450364682240000, 13106744139423334400000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS For n > 0: a(3*n)   = A032031(3*n) = 3^(3*n) * Gamma(3*n + 1). a(3*n-1) = A008544(3*n-1) = 3^(3*n-1) * Gamma(3*n - 1/3) / Gamma(2/3). a(3*n+1) = A007559(3*n+1) = 3^(3*n+3/2) * Gamma(3*n + 4/3) * Gamma(2/3) / (2*Pi). LINKS Peter Luschny, Multifactorials FORMULA From Johannes W. Meijer, Jul 04 2011: (Start) a(3*n+3)/(a(3*n)*a(3)) = A006566(n+1); Dodecahedral numbers a(3*n+4)/a(3*n+1) = A136214(3*n+4, 3*n+1) a(3*n+5)/a(3*n+2) = A112333(3*n+5, 3*n+2) (End) MAPLE 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); MATHEMATICA a[n_] := Switch[Mod[n, 3], 0, 3^n Gamma[n+1], 2, 3^n Gamma[n+2/3]/ Gamma[2/3], 1, 3^(n-1) Gamma[n+1/3]/Gamma[4/3]] // Round; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Jun 25 2019 *) PROG (PARI) a(n) = vecprod(vector(3*n, k, if (k % 3 == n % 3, k, 1))); \\ Michel Marcus, Jun 25 2019 CROSSREFS Cf. A190901. Sequence in context: A034724 A234283 A074703 * A303486 A064747 A285995 Adjacent sequences:  A190900 A190901 A190902 * A190904 A190905 A190906 KEYWORD nonn AUTHOR Peter Luschny, Jul 03 2011 STATUS approved

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Last modified December 9 17:18 EST 2019. Contains 329879 sequences. (Running on oeis4.)