

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
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OFFSET

0,3


COMMENTS

For n > 0:
a(3*n) = A032031(3*n) = 3^(3*n) * Gamma(3*n + 1).
a(3*n1) = A008544(3*n1) = 3^(3*n1) * 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

Table of n, a(n) for n=0..17.
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^(n1) Gamma[n+1/3]/Gamma[4/3]] // Round;
Table[a[n], {n, 0, 20}] (* JeanFrançois 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



