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A297892
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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.
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0
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1, 1, 2, 1, 24, 14, 1, 234, 1638, 236, 1, 2160, 147420, 254880, 12692, 1, 19602, 12349260, 208173240, 124394292, 1783784, 1, 176904, 1011404394, 157378969440, 916910326332, 157779262368, 811523288
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OFFSET
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0,3
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LINKS
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FORMULA
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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.
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EXAMPLE
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Triangle begins
1;
1, 2;
1, 24, 14;
1, 234, 1638, 236;
1, 2160, 147420, 254880, 12692;
1, 19602, 12349260, 208173240, 124394292, 1783784;
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MATHEMATICA
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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[
z^r/g[r], {r, 0, nn}], {z, 0, nn}], {z, u}]]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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