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

1,4

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.

Links

Table of n, a(n) for n=1..23.

Prog

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

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.

Sequence in context: A012313 A012517 A012314 * A012360 A012708 A009077

Adjacent sequences: A233001 A233002 A233003 * A233005 A233006 A233007

Keyword

nonn

Author

Alex Ratushnyak, Dec 03 2013

Status

approved