A217649 a(n) = n!! mod n!!!

0, 0, 0, 0, 0, 5, 12, 21, 64, 135, 200, 715, 1368, 455, 4480, 14985, 13440, 111265, 511920, 752115, 425600, 4278015, 1379840, 38386425, 165473280, 35660625, 1921920000, 2430686475, 1614412800, 8228995775, 42652915200, 375052302625, 40180940800, 221238396225

Offset

0,6

Comments

n !! is a double factorial number (see the definition in A006882).

n !!! is a triple factorial number (see the definition in A007661).

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Example

a(7) = 21 because 7!! = 105, 7!!! = 28 => 105 == 21 mod 28.

Maple

A:= n -> mul(k, k = select(k -> k mod 3 = n mod 3, [$1 .. n])): for m from 0 to 80 do:
z:= irem(m!, A(m)):printf(`%d, `, z):od:

Mathematica

multiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*multiFactorial[n - k, k]]]; Table[Mod[n!!, multiFactorial[n, 3]], {n, 0, 35} ]
Table[Mod[n!!, Times@@Range[n, 1, -3]], {n, 0, 40}] (* Harvey P. Dale, Mar 06 2021 *)

Crossrefs

Cf. A006882, A007661.

Sequence in context: A345879 A345714 A242338 * A333578 A131976 A074376

Adjacent sequences: A217646 A217647 A217648 * A217650 A217651 A217652

Keyword

nonn

Author

Michel Lagneau, Oct 09 2012

Status

approved