A105350
Largest squared factorial dividing n!.
Original entry on oeis.org
1, 1, 1, 1, 4, 4, 36, 36, 576, 576, 518400, 518400, 518400, 518400, 25401600, 25401600, 1625702400, 1625702400, 131681894400, 131681894400, 13168189440000, 13168189440000, 1593350922240000, 1593350922240000, 229442532802560000, 229442532802560000
Offset: 0
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a[n_] := (For[k = 1, Divisible[n!, k!^2], k++]; (k-1)!^2)
Table[a[n], {n, 0, 24}] (* Jean-François Alcover, Aug 07 2018 *)
A182923
a(n) = n$ / A055773(n), where n$ denotes the swinging factorial (A056040).
Original entry on oeis.org
1, 1, 1, 1, 2, 2, 4, 4, 2, 18, 36, 36, 12, 12, 24, 360, 90, 90, 20, 20, 4, 84, 168, 168, 28, 700, 1400, 37800, 5400, 5400, 720, 720, 90, 2970, 5940, 207900, 23100, 23100, 46200, 1801800, 180180, 180180, 17160
Offset: 0
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swingfact := n -> n! / iquo(n,2)!^2;
A182923 := n -> swingfact(n) / mul(k, k=select(isprime, [$iquo(n,2)+1..n])):
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sf[n_] := n!/Floor[n/2]!^2;
a[n_] := sf[n]/Numerator[n!/Floor[n/2]!^4];
Table[a[n], {n, 0, 42}] (* Jean-François Alcover, Jun 22 2019 *)
A349269
Triangle read by rows, T(n, k) = (n - k)! * k! / floor(k / 2)! ^ 2.
Original entry on oeis.org
1, 1, 1, 2, 1, 2, 6, 2, 2, 6, 24, 6, 4, 6, 6, 120, 24, 12, 12, 6, 30, 720, 120, 48, 36, 12, 30, 20, 5040, 720, 240, 144, 36, 60, 20, 140, 40320, 5040, 1440, 720, 144, 180, 40, 140, 70, 362880, 40320, 10080, 4320, 720, 720, 120, 280, 70, 630
Offset: 0
[0] 1;
[1] 1, 1;
[2] 2, 1, 2;
[3] 6, 2, 2, 6;
[4] 24, 6, 4, 6, 6;
[5] 120, 24, 12, 12, 6, 30;
[6] 720, 120, 48, 36, 12, 30, 20;
[7] 5040, 720, 240, 144, 36, 60, 20, 140;
[8] 40320, 5040, 1440, 720, 144, 180, 40, 140, 70;
[9] 362880, 40320, 10080, 4320, 720, 720, 120, 280, 70, 630;
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T := (n, k) -> (n - k)!*k! / iquo(k,2)! ^ 2:
seq(seq(T(n, k), k = 0..n), n = 0..9);
Showing 1-3 of 3 results.
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