login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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^(n-1) Gamma[n+1/3]/Gamma[4/3]] // Round;

Table[a[n], {n, 0, 20}] (* Jean-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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