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%I #8 Feb 10 2026 15:48:43
%S 1,2,10,218,22906,10651322,20802031930,166437057472058,
%T 5390064106232598586,702352303362638758749242,
%U 367156773639729499052442504250,768856023700258389105237851742346298,6444908708706586437631037608905406860868666
%N Number of n X n matrices over GF(2) such that the row space is equal to the column space.
%F a(n) = Sum_{k=0..n} A002884(k)*A022166(n,k).
%t nn = 12; B[n_] := QFactorial[n, 2];e[z_] := Sum[z^n/B[n], {n, 0, nn}]; A[z_] := Sum[Product[2^n - 2^i, {i, 0, n - 1}] z^n/B[n], {n, 0, nn}];Table[B[n], {n, 0, nn}] CoefficientList[Series[A[z]*e[z], {z, 0, nn}], z]
%Y Cf. A002884, A022166.
%K nonn
%O 0,2
%A _Geoffrey Critzer_, Feb 05 2026