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A233004 Pt(n) mod n!, where Pt(n) is product of first n positive triangular numbers (A000217). 0
0, 1, 0, 12, 60, 540, 0, 20160, 181440, 907200, 19958400, 359251200, 1556755200, 32691859200, 0, 10461394944000, 177843714048000, 1600593426432000, 60822550204416000, 608225502044160000, 38318206628782080000, 702500454861004800000, 12926008369442488320000 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 6 15:57 EDT 2022. Contains 355111 sequences. (Running on oeis4.)