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

Author

Alex Ratushnyak, Dec 03 2013

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

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

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

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

Programs

Python

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