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Triangular array read by rows. T(n,k) is the number of n X n matrices A over F_2 such that Sum_{phi} nullity(phi(A)) = k where the sum is over all monic irreducible polynomials in F_2[x] that divide the characteristic polynomial of A, n >= 1, 1 <= k <= n.
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%I #11 Dec 15 2022 14:02:24

%S 2,6,10,84,210,218,5040,19740,15330,25426,1249920,5780880,6939660,

%T 7604610,11979362,1259919360,7533267840,9297061200,12276675180,

%U 14280964866,24071588290,5120312279040,34082078607360,48312946523520,78970351980240,88215877158444,112601184828930,195647202043778

%N Triangular array read by rows. T(n,k) is the number of n X n matrices A over F_2 such that Sum_{phi} nullity(phi(A)) = k where the sum is over all monic irreducible polynomials in F_2[x] that divide the characteristic polynomial of A, n >= 1, 1 <= k <= n.

%e Triangle begins

%e 2;

%e 6, 10;

%e 84, 210, 218;

%e 5040, 19740, 15330, 25426;

%e 1249920, 5780880, 6939660, 7604610, 11979362;

%e ...

%Y Cf. A346222 (main diagonal), A083402 (1/2 * column 1), A002416 (row sums).

%K nonn,tabl

%O 1,1

%A _Geoffrey Critzer_, Nov 29 2022