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A356583
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.
1
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, 10, 10, 22, 0, 64, 20, 4, 10, 10, 20, 22, 42, 0, 128, 20, 18, 6, 24, 16, 44, 42, 86, 0, 256, 40, 14, 18, 18, 48, 38, 80, 86, 170, 0, 512, 40, 36, 16, 48, 32, 106, 68, 166, 170, 342, 0, 1024
OFFSET
0,3
FORMULA
G.f.: Product_{i>=1} (1/(1-x^i) - x^i + y^i*x^i)^A001037(i).
EXAMPLE
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, 10, 10, 22, 0, 64;
MATHEMATICA
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
CROSSREFS
Cf. A001037.
Sequence in context: A354186 A366265 A127527 * A217943 A177225 A236306
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Aug 13 2022
STATUS
approved