A086699 - OEIS

%I #17 Dec 15 2024 19:49:20

%S 1,9,294,37800,19373760,39687459840,325139829719040,

%T 10654345790226432000,1396491759480328106803200,

%U 732164571206732295657278668800,1535460761275478347250381697633484800,12880379193826999985837000446453418557440000

%N Number of n X n matrices over GF(2) with rank n-1.

%C a(n)/2^(n^2) is the probability that a random linear operator T on an n dimensional vector space over the field with two elements is such that the dimension of the range of T equals n-1.  This probability is Product{j>=2} 1 - 1/2^j which is 2 times the probability that the dimension of the range of T equals n. Cf. A048651. - _Geoffrey Critzer_, Jun 28 2017

%H Vincenzo Librandi, <a href="/A086699/b086699.txt">Table of n, a(n) for n = 1..58</a>

%F for n>=2 : a(n) = product j=0...n-2 (2^n - 2^j)^2 / (2^(n-1)- 2^j).

%t Table[Product[(q^n - q^i)^2/(q^(n - 1) - q^i), {i, 0, n - 2}] /.  q -> 2, {n, 0, 15}] (* _Geoffrey Critzer_, Jun 28 2017 *)

%o (PARI) a(n) = prod(j=0, n-2, (2^n - 2^j)^2 / (2^(n-1)- 2^j)); \\ _Michel Marcus_, Jun 28 2017

%Y Cf. A002884, A060867.

%K nonn

%O 1,2

%A Yuval Dekel (dekelyuval(AT)hotmail.com), Jul 28 2003

%E More terms from _David Wasserman_, Mar 28 2005