%I #9 Jul 09 2018 11:10:10
%S 1,21,1141,208965,139889701,354550756581,3464730268306021,
%T 131934922593867875685,19707939574875773323508581,
%U 11599530748705611712884878698341,26983642577843418550426409405086580581,248652621703069011230281370429818425958461285
%N Sum of rank(M) over all n X n matrices over GF(2).
%C a(n) <= A086875(n).
%H Andrew Howroyd, <a href="/A086098/b086098.txt">Table of n, a(n) for n = 1..50</a>
%H Kent E. Morrison, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Morrison/morrison37.html">Integer Sequences and Matrices Over Finite Fields</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
%F For prime power q the number of rank-r n X n matrices over GF(q) is F(r, n) = product j=0..(r-1) (q^n-q^j)^2/(q^r-q^j) so a(n) = sum r=1..n r*product j=0..(r-1) (q^n-q^j)^2/(q^r-q^j) . In this case q=2.
%F a(n) = Sum_{r=1..n} r*Product_{j=0, r-1} (2^n - 2^j)^2/(2^r - 2^j). - _Andrew Howroyd_, Jul 08 2018
%o (PARI) a(n) = {my(q=2); sum(r=1, n, r*prod(j=0, r-1, (q^n-q^j)^2/(q^r-q^j)))} \\ _Andrew Howroyd_, Jul 08 2018
%Y Cf. A086190, A086207, A086875.
%K nonn
%O 1,2
%A Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 24 2003
%E Terms a(8) and beyond from _Andrew Howroyd_, Jul 08 2018