A085529
a(n) = (2n+1)^(2n+1).
Original entry on oeis.org
1, 27, 3125, 823543, 387420489, 285311670611, 302875106592253, 437893890380859375, 827240261886336764177, 1978419655660313589123979, 5842587018385982521381124421, 20880467999847912034355032910567, 88817841970012523233890533447265625, 443426488243037769948249630619149892803
Offset: 0
Cf.
A000312,
A005408,
A016754,
A085527,
A085528,
A085530,
A085531,
A085532,
A085533,
A085534,
A085535.
A347281
a(n) = 2^(n - 1)*permanent(M_n)^2 where M_n is the n X n matrix M_n(j, k) = cos(Pi*j*k/n).
Original entry on oeis.org
1, 2, 4, 0, 36, 288, 144, 18432, 11664, 115200, 144400, 0, 808151184, 133693952, 262440000, 299649466368, 7937314520976, 73575242956800, 21204146201616, 6459752448000000, 212406372892224, 8753824001424826368, 195844025123172289600, 152252829159294763008, 26487254903393025000000
Offset: 1
a(7) = -3384288*cos(Pi/7) - 3460896*sin(Pi/14) - 45888*cos(2*Pi/7) - 28224*cos(15*Pi/7) + 48384*cos(17*Pi/7) + 1706400 + 3458400*sin(3*Pi/14) = 144. - _Chai Wah Wu_, Sep 19 2021
-
P(n)=matpermanent(matrix(n,n,j,k,cos((Pi*j*k)/n)));
for(k=1,25,print1(round(2^(k-1)*P(k)^2),", "))
A371153
a(n) is the permanent of the 2n+1 X 2n+1 matrix P(2n+1) defined by P[1,j] = 1, P[i,j] = i-1 if i<=j, and P[i,i] = i-n-1 otherwise with 1 <= i,j <= 2n+1.
Original entry on oeis.org
1, -3, 185, -55307, 49980969, -106782742099, 462446644072153, -3649813053096346875, 48540310969531346254217, -1024268653171975469599364291, 32694499032613728282606987622521, -1518591968826504411972243578217645163, 99392870823564324693001427592486103515625
Offset: 0
a(3) = -55307:
1, 1, 1, 1, 1, 1, 1;
-6, 1, 1, 1, 1, 1, 1;
-5, -5, 2, 2, 2, 2, 2;
-4, -4, -4, 3, 3, 3, 3;
-3, -3, -3, -3, 4, 4, 4;
-2, -2, -2, -2, -2, 5, 5;
-1, -1, -1, -1, -1, -1, 6.
-
b[n_]:=Permanent[Table[If[i==1, 1, If[i<=j, i-1, i-n-1]], {i, n}, {j, n}]]; a[n_]:=b[2n+1]; Array[a, 10,0]
Showing 1-3 of 3 results.
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