A233003 (n!)^2 mod Pt(n), where Pt(n) is product of first n positive triangular numbers (A000217).

0, 1, 0, 36, 900, 8100, 0, 25401600, 514382400, 12859560000, 6224027040000, 56016243360000, 9466745127840000, 1855482045056640000, 0, 6679735362203904000000, 13513104637738497792000000, 156365925093831188736000000, 225792395835492236534784000000, 22579239583549223653478400000000

Offset

1,4

Comments

Indices of zeros appear to be 2^k-1.

Links

Table of n, a(n) for n=1..20.

Example

a(4) = 1*4*9*16 mod 1*3*6*10 = 576 mod 90 = 36.

Prog

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

Crossrefs

Cf. A000142, A000217, A000290, A001044(n!^2).

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

Cf. A006788 (floor(n!^2/Pt)).

Sequence in context: A169836 A335220 A248108 * A075916 A062150 A011811

Adjacent sequences: A233000 A233001 A233002 * A233004 A233005 A233006

Keyword

nonn

Author

Alex Ratushnyak, Dec 03 2013

Status

approved