A356583 - OEIS

%I #17 Aug 23 2022 10:20:53

%S 1,0,2,2,0,2,2,2,0,4,4,2,2,0,8,4,4,2,6,0,16,10,2,4,6,10,0,32,8,10,4,

%T 10,10,22,0,64,20,4,10,10,20,22,42,0,128,20,18,6,24,16,44,42,86,0,256,

%U 40,14,18,18,48,38,80,86,170,0,512,40,36,16,48,32,106,68,166,170,342,0,1024

%N T(n,k) is the number of degree n polynomials p in GF_2[x] whose squarefree part has degree k, n >= 0, 0 <= k <= n. Triangular array read by rows.

%F G.f.: Product_{i>=1} (1/(1-x^i) - x^i + y^i*x^i)^A001037(i).

%e    1;

%e    0,  2;

%e    2,  0, 2;

%e    2,  2, 0,  4;

%e    4,  2, 2,  0,  8;

%e    4,  4, 2,  6,  0, 16;

%e   10,  2, 4,  6, 10,  0, 32;

%e    8, 10, 4, 10, 10, 22,  0, 64;

%t nn = 12; q = 2; a = Table[1/n Sum[MoebiusMu[n/d] q^d, {d, Divisors[n]}], {n, 1, nn}]; Table[Take[CoefficientList[ Series[Product[(1/(1 -  z^i) - z^i + u^i z^i)^a[[i]], {i, 1,nn}], {z, 0, nn}], {z, u}][[j]], j], {j, 1, nn}] // Grid

%Y Cf. A001037.

%K nonn,tabl

%O 0,3

%A _Geoffrey Critzer_, Aug 13 2022