OFFSET
0,3
COMMENTS
Row m = 1 counts the squarefree monic polynomials of degree n in GF_2[x] which is the main diagonal of A356583.
LINKS
Kent E. Morrison, Random polynomials over finite fields, 1999.
FORMULA
For n>m, T(m,n) = 2^n - 2^(n-m).
G.f. for row m: (1/(1-2x))*Product_{n>=1}(1-x^(n(m+1)))^A001037(n).
EXAMPLE
1, 2, 2, 4, 8, 16, 32, 64, 128, 256, 512,
1, 2, 4, 6, 12, 24, 48, 96, 192, 384, 768,
1, 2, 4, 8, 14, 28, 56, 112, 224, 448, 896,
1, 2, 4, 8, 16, 30, 60, 120, 240, 480, 960,
1, 2, 4, 8, 16, 32, 62, 124, 248, 496, 992,
1, 2, 4, 8, 16, 32, 64, 126, 252, 504, 1008,
1, 2, 4, 8, 16, 32, 64, 128, 254, 508, 1016,
1, 2, 4, 8, 16, 32, 64, 128, 256, 510, 1020,
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1022,
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024
MATHEMATICA
nn = 12; a[q_, r_] := 1/r Sum[MoebiusMu[r/d] q^d, {d, Divisors[r]}]; mfree =
Table[CoefficientList[Series[1/(1 -q t) Product[((1 - t^n) Sum[(t^ n)^l, {l, 0, m}])^a[q, n], {n, 1, nn}] /. q -> 2, {t, 0, nn}], t], {m, 1, nn}];
Table[Table[mfree[[m + 1 - i, i]], {i, 1, m}], {m, 1, nn}] // Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Aug 18 2022
STATUS
approved