A233004 Pt(n) mod n!, where Pt(n) is product of first n positive triangular numbers (A000217).

0, 1, 0, 12, 60, 540, 0, 20160, 181440, 907200, 19958400, 359251200, 1556755200, 32691859200, 0, 10461394944000, 177843714048000, 1600593426432000, 60822550204416000, 608225502044160000, 38318206628782080000, 702500454861004800000, 12926008369442488320000

Offset: 1

Author

Alex Ratushnyak, Dec 03 2013

Keywords

• nonn

Comments

Pt(n) = n!*(n+1)! / 2^n.

Pt(n) mod n! = 0 if and only if 2^n divides (n+1)!, that is, n+1 is a power of 2. Thus indices of zeros are of the form 2^k-1.

Crossrefs

Cf. A000142, A000217.

Cf. A006472 (triangular factorial, essentially equal to Pt(n)).

Cf. A067667 (Pt(n)/n! for n's of the form 2^k-1).

Cf. A069902, A007917.

Programs

Python

f=t=1
for n in range(1,33):
  t*=n*(n+1)//2
  f*=n
  print(t%f, end=', ')