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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).

%I A083402 #9 Feb 17 2014 06:02:48
%S A083402 1,3,42,2520,624960,629959680,2560156139520,41781748196966400,
%T A083402 2732860586067178291200,715703393163961188325785600,
%U A083402 750102961052993818881476159078400,3145391744524297920839316348340273152000,52764474940208177704130232748554603290689536000
%N 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).
%H A083402 Eric M. Schmidt, <a href="/A083402/b083402.txt">Table of n, a(n) for n = 1..30</a>
%F A083402 a(n) = A002884(n) / 2^(n-1).
%e A083402 For example for n=4 the matrix is / 1,1,1,1 / 0,1,1,1 / 0,0,1,1 / 0,0,0,1 /.
%p A083402 a:= n-> 2^((n-1)*(n-2)/2) *mul(2^k-1, k=1..n):
%p A083402 seq(a(n), n=1..15);  # _Alois P. Heinz_, May 14 2013
%t A083402 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_ *)
%Y A083402 Cf. A002884, A070731, A082877, A062383.
%K A083402 nonn
%O A083402 1,2
%A A083402 Yuval Dekel (dekelyuval(AT)hotmail.com), Jun 12 2003
%E A083402 More terms from _Eric M. Schmidt_, May 14 2013