login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A175567 (n!)^2 modulo n(n+1)/2. 3
0, 1, 0, 6, 0, 15, 0, 0, 0, 45, 0, 66, 0, 0, 0, 120, 0, 153, 0, 0, 0, 231, 0, 0, 0, 0, 0, 378, 0, 435, 0, 0, 0, 0, 0, 630, 0, 0, 0, 780, 0, 861, 0, 0, 0, 1035, 0, 0, 0, 0, 0, 1326, 0, 0, 0, 0, 0, 1653, 0, 1770, 0, 0, 0, 0, 0, 2145, 0, 0, 0, 2415, 0, 2556, 0, 0, 0, 0, 0, 3003, 0, 0, 0, 3321 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

It appears that if n is one less than an odd prime then (n!)^2 modulo n(n+1)/2 is n(n-1)/2 else 0. This result appears to hold for any even power of n!. See A119690 for similar results related to odd powers of n!.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

MATHEMATICA

Table[Mod[(n!)^2, (n^2 + n)/2], {n, 100}] (* Vincenzo Librandi, Jul 10 2014 *)

Table[PowerMod[n!, 2, (n(n+1))/2], {n, 100}] (* Harvey P. Dale, Aug 27 2016 *)

PROG

(PARI) a(n) = (n!)^2 % (n*(n+1)/2); \\ Michel Marcus, Jul 09 2014

CROSSREFS

Cf. A119690, A169690, A175553.

Sequence in context: A320146 A283999 A240813 * A069828 A270536 A278712

Adjacent sequences:  A175564 A175565 A175566 * A175568 A175569 A175570

KEYWORD

nonn

AUTHOR

John W. Layman, Jul 12 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 14:15 EST 2019. Contains 329806 sequences. (Running on oeis4.)