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 A156603 A q-factorial triangle sequence built of Cartan A_n polynomials as antidiagonals: p(x,n)=CartanAn(x,n): t(n,k)=If[m == 0, n!, Product[p(m+1),k), {k, 1, n}]]; 0

%I

%S 1,1,1,1,1,2,1,1,0,6,1,1,-1,0,24,1,1,-2,0,0,120,1,1,-3,-6,0,0,720,1,1,

%T -4,-24,24,0,0,5040,1,1,-5,-60,504,120,0,0,40320,1,1,-6,-120,3360,

%U 27720,-720,0,0,362880,1,1,-7,-210,13800,702240,-3991680,-5040,0,0,3628800

%N A q-factorial triangle sequence built of Cartan A_n polynomials as antidiagonals: p(x,n)=CartanAn(x,n): t(n,k)=If[m == 0, n!, Product[p(m+1),k), {k, 1, n}]];

%C Row sums are:

%C {1, 2, 4, 8, 25, 120, 713, 5038, 40881, 393116, 347905,...}.

%F p(x,n)=CartanAn(x,n):

%F t(n,k)=If[m == 0, n!, Product[p(m+1),k), {k, 1, n}]];

%F Out_(n,m)=antidiagonal(t(n,m)).

%e {1},

%e {1, 1},

%e {1, 1, 2},

%e {1, 1, 0, 6},

%e {1, 1, -1, 0, 24},

%e {1, 1, -2, 0, 0, 120},

%e {1, 1, -3, -6, 0, 0, 720},

%e {1, 1, -4, -24, 24, 0, 0, 5040},

%e {1, 1, -5, -60, 504, 120, 0, 0, 40320},

%e {1, 1, -6, -120, 3360, 27720, -720, 0, 0, 362880},

%e {1, 1, -7, -210, 13800, 702240, -3991680, -5040, 0, 0, 3628800}

%t Clear[t, n, m, i, k, a, b, T, M, p];

%t T[n_, m_, d_] := If[ n == m, 2, If[n == m - 1 || n == m + 1, -1, 0]];

%t M[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}];

%t p[x_, n_] := If[n == 0, 1, CharacteristicPolynomial[M[n], x]];

%t a0 = Table[p[x, n], {n, 0, 20}] /. x -> m + 1;

%t t[n_, m_] = If[m == 0, n!, Product[a0[[k]], {k, 1, n}]];

%t a = Table[Table[t[n, m], {n, 0, 10}], {m, 0, 10}];

%t b = Table[Table[a[[m, n - m + 1]], {m, n, 1, -1}], {n, 1, Length[a]}]'

%t Flatten[%]

%Y A034801, A156599, A156600, A156601, A156602

%K sign,tabl,uned

%O 0,6

%A _Roger L. Bagula_, Feb 11 2009

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Last modified May 8 02:26 EDT 2021. Contains 343652 sequences. (Running on oeis4.)