A302346 Triangle read by rows. Number of invertible linear operators T on an n-dimensional vector space over GF(2) such that T(U) = U for some given k-dimensional subspace U.

1, 1, 1, 6, 2, 6, 168, 24, 24, 168, 20160, 1344, 576, 1344, 20160, 9999360, 322560, 64512, 64512, 322560, 9999360, 20158709760, 319979520, 30965760, 14450688, 30965760, 319979520, 20158709760

Offset

0,4

Links

Table of n, a(n) for n=0..27.

Formula

T(n,k) = A002884(k)*A002884(n-k)*2^(k*(n-k)).

Example

Triangle T(n,k) begins:
        1;
        1,      1;
        6,      2,     6;
      168,     24,    24,   168;
    20160,   1344,   576,  1344,  20160;
  9999360, 322560, 64512, 64512, 322560, 9999360;
  ...

Mathematica

f[n_, k_] := \[Gamma][k] \[Gamma][n - k] q^(k (n - k)); \[Gamma][n_] := Product[q^n - q^i, {i, 0, n - 1}];
Table[Table[f[n, k], {k, 0, n}], {n, 0, 6}] // Grid

Crossrefs

Cf. A002884, A302339.

Sequence in context: A021945 A002371 A048595 * A340421 A244922 A153313

Adjacent sequences: A302343 A302344 A302345 * A302347 A302348 A302349

Keyword

nonn,tabl

Author

Geoffrey Critzer, Apr 05 2018

Status

approved