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

1,2

Links

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

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

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 *)

Prog

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

Crossrefs

Cf. A000142, A000292, A119690.

Sequence in context: A130190 A110346 A095754 * A181159 A127320 A098917

Adjacent sequences: A226715 A226716 A226717 * A226719 A226720 A226721

Keyword

nonn,easy

Author

Alex Ratushnyak, Jun 15 2013

Status

approved