A083402 Let A_n be the upper triangular matrix in the group GL(n,2) that has zero entries below the main diagonal and 1 elsewhere; a(n) is the size of the conjugacy class of this matrix in GL(n,2).

1, 3, 42, 2520, 624960, 629959680, 2560156139520, 41781748196966400, 2732860586067178291200, 715703393163961188325785600, 750102961052993818881476159078400, 3145391744524297920839316348340273152000, 52764474940208177704130232748554603290689536000

Offset: 1

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Jun 12 2003

Keywords

• nonn

Examples

			For example for n=4 the matrix is / 1,1,1,1 / 0,1,1,1 / 0,0,1,1 / 0,0,0,1 /.
		

Links

• Eric M. Schmidt, Table of n, a(n) for n = 1..30

Crossrefs

Cf. A002884, A070731, A082877, A062383.

Programs

Maple

a:= n-> 2^((n-1)*(n-2)/2) *mul(2^k-1, k=1..n):
seq(a(n), n=1..15);  # Alois P. Heinz, May 14 2013

Mathematica

a[n_] := 2^((n-1)*(n-2)/2)*Product[2^k-1, {k, 1, n}]; Table[a[n], {n, 1, 15}] (* Jean-François Alcover, Feb 17 2014, after Alois P. Heinz *)

Formula

a(n) = A002884(n) / 2^(n-1).

Extensions

More terms from Eric M. Schmidt, May 14 2013