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A297892 Triangle read by rows. T(n,k) is the number of n X n diagonalizable matrices over GF(3) that have rank k, 0 <= k <= n, n >= 0.

%I A297892 #21 Aug 02 2018 16:36:02
%S A297892 1,1,2,1,24,14,1,234,1638,236,1,2160,147420,254880,12692,1,19602,
%T A297892 12349260,208173240,124394292,1783784,1,176904,1011404394,
%U A297892 157378969440,916910326332,157779262368,811523288
%N A297892 Triangle read by rows.  T(n,k) is the number of n X n diagonalizable matrices over GF(3) that have rank k, 0 <= k <= n, n >= 0.
%H A297892 Geoffrey Critzer, <a href="https://esirc.emporia.edu/handle/123456789/3595">Combinatorics of Vector Spaces over Finite Fields</a>, Master's thesis, Emporia State University, 2018.
%H A297892 Kent E. Morrison, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Morrison/morrison37.html">Integer Sequences and Matrices Over Finite Fields</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
%F A297892 T(n,k)/A053290(n) is the coefficient of y^k*x^n in the expansion of Sum_{n>=0} x^n\A053290(n) * (Sum_{n>=0} y*x^n\A053290(n))^2.
%e A297892 Triangle begins
%e A297892   1;
%e A297892   1,     2;
%e A297892   1,    24,       14;
%e A297892   1,   234,     1638,       236;
%e A297892   1,  2160,   147420,    254880,     12692;
%e A297892   1, 19602, 12349260, 208173240, 124394292, 1783784;
%t A297892 nn = 5; g[n_] := (q - 1)^n  q^Binomial[n, 2] FunctionExpand[QFactorial[n, q]] /. q -> 3;G[n] := Sum[u z^r/g[r], {r, 0, nn}]; Grid[Map[Select[#, # > 0 &] &,Table[g[n], {n, 0, nn}] CoefficientList[Series[Sum[(u z)^r/g[r] , {r, 0, nn}]^2 Sum[
%t A297892        z^r/g[r], {r, 0, nn}], {z, 0, nn}], {z, u}]]]
%Y A297892 Cf. A296548, A053846 (main diagonal), A290516 (row sums).
%K A297892 nonn,tabl
%O A297892 0,3
%A A297892 _Geoffrey Critzer_, Jan 07 2018