OFFSET
0,3
COMMENTS
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
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) = prod(k=1, 3*n, if (k % 3 == n % 3, k, 1)); \\ Michel Marcus, Jun 25 2019 and May 14 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Jul 03 2011
STATUS
approved