%I #10 May 29 2022 18:07:11

%S 1,1,5,146,17352,8607552,17362252800,141087882903552,

%T 4605333486987902976,602440395156024780128256,

%U 315546297657431573076891402240,661423879140352987222707528171257856,5547073628722488310034844542685201882415104,186106159461598495645613441708238958650047305089024

%N Number of invertible n X n cyclic matrices over GF(2).

%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 Sum_{n>=0} a(n)x^n/A002884(n) = (1 + 2x/(2-x)* Product_{i>=2}(1 + x^i/((2^i-1)(1-x/2)^i)))^A001037(i).

%t nn = 13; A001037 = Table[1/n Sum[MoebiusMu[n/d] 2^d, {d, Divisors[n]}], {n, 1, nn}];Table[Product[2^n - 2^i, {i, 0, n - 1}], {n, 0, nn}]CoefficientList[Series[(1 + 2 x/(2 - x)) Product[(1 + 2^i x^i/((2^i - 1) (2^i - x^i)))^ A001037[[i]], {i, 2, nn}], {x, 0, nn}], x]

%Y Cf. A001037, A002884, A346082.

%K nonn

%O 0,3

%A _Geoffrey Critzer_, Jul 04 2021