A063709 -id:A063709 - cp's OEIS frontend

A064546 Remainder when (n!)^2 is divided by n^n.

0, 0, 9, 64, 1900, 5184, 695310, 15089664, 346348629, 8189440000, 170553548176, 4519967588352, 202522159449675, 8500218417954816, 265594041953296875, 3543051899458551808, 454740628232312103872, 5853583711033675481088, 1445271811400044958489895, 91546885417441689600000000

Offset: 1

Floor van Lamoen, Oct 09 2001

nonn

			a(5) = 1900 because (5!)^2 = 14400 = 1900 (mod 5^5 = 3125).

Harry J. Smith, Table of n, a(n) for n = 1..100

Cf. A063709, A215460.

A064546[n_] := PowerMod[n!, 2, n^n];
Array[A064546, 20] (* Paolo Xausa, Aug 05 2025 *)

{ for (n=1, 100, write("b064546.txt", n, " ", (n!)^2 % n^n) ) } \\ Harry J. Smith, Sep 18 2009

a(n) = (n!)^2 mod n^n.

A215460 a(n) = floor(n!^2 / n^n).

Original entry on oeis.org

1, 1, 1, 2, 4, 11, 30, 96, 339, 1316, 5584, 25733, 128025, 683949, 3905083, 23731187, 152934464, 1041782238, 7479469995, 56448098958, 446768591341, 3700276748921, 32007269639380, 288630046441757, 2708888570942365, 26419890078249485, 267389254029561667, 2804508541393392135, 30446382653772707171, 341729529206733994569

Offset: 1

Alex Ratushnyak, Aug 11 2012

nonn

			a(4) = floor((4!)^2 / (4^4)) = floor(24^2 / 256) = floor(2.25) = 2.

Paolo Xausa, Table of n, a(n) for n = 1..500

Cf. A064546, A063709, A055775.

A215460[n_] := Quotient[n!^2, n^n];
Array[A215460, 30] (* Paolo Xausa, Aug 05 2025 *)

f = 1
for n in range(1,33):
    print(f*f // n**n)
    f *= n+1

More terms from Paolo Xausa, Aug 05 2025

A211341 a(n) = (n^n mod n!)/n.

Original entry on oeis.org

0, 0, 1, 4, 1, 96, 289, 512, 25281, 265600, 2391001, 36972288, 405301681, 21023744, 54720993825, 1244339070976, 13293650868481, 324381631315968, 2266027617084841, 14819020931072000, 896776708870156401

Offset: 1

Alexander R. Povolotsky, Mar 10 2013

nonn

G. C. Greubel, Table of n, a(n) for n = 1..445

Cf. A063709.

Table[Mod[n^n, n!]/n, {n,50}] (* G. C. Greubel, Feb 25 2017 *)

a(n) = A063709(n)/n. - Michel Marcus, Feb 25 2017

cp's OEIS Frontend

A064546 Remainder when (n!)^2 is divided by n^n.

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A215460 a(n) = floor(n!^2 / n^n).

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A211341 a(n) = (n^n mod n!)/n.

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Mathematica

Formula