A226718 n! mod tetrahedral(n), that is A000142(n) mod A000292(n).

0, 2, 6, 4, 15, 48, 0, 0, 45, 120, 66, 168, 0, 0, 120, 288, 153, 360, 0, 0, 231, 528, 0, 0, 0, 0, 378, 840, 435, 960, 0, 0, 0, 0, 630, 1368, 0, 0, 780, 1680, 861, 1848, 0, 0, 1035, 2208, 0, 0, 0, 0, 1326, 2808, 0, 0, 0, 0, 1653, 3480, 1770, 3720, 0, 0, 0, 0, 2145, 4488

Offset: 1

Author

Alex Ratushnyak, Jun 15 2013

Keywords

• nonn
• easy

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000142, A000292, A119690.

Programs

Maple

A226718 := proc(n)
    n! mod ( n*(n+1)*(n+2)/6) ;
end proc: # R. J. Mathar, Jun 18 2013

Mathematica

Table[Mod[n!, n (n + 1) (n + 2)/6], {n, 66}] (* Ivan Neretin, May 18 2015 *)

Python

f = 1
for i in range(1, 100):
    f *= i
    print(f % (i*(i+1)*(i+2)//6), end=', ')

Formula

a(n) = n! mod (n*(n+1)*(n+2)/6).

For n>4: if neither n+1 nor n+2 is prime, then a(n)=0. Otherwise, a(n)=n(n+1)/2 for odd n and a(n)=n(n+2) for even n. - Ivan Neretin, May 18 2015