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A076756 Triangle of coefficients of characteristic polynomial of M_n, the n X n matrix M_(i,j) = min(i,j).

%I A076756 #39 Oct 27 2023 21:41:11
%S A076756 1,-1,1,1,-3,1,-1,5,-6,1,1,-7,15,-10,1,-1,9,-28,35,-15,1,1,-11,45,-84,
%T A076756 70,-21,1,-1,13,-66,165,-210,126,-28,1,1,-15,91,-286,495,-462,210,-36,
%U A076756 1,-1,17,-120,455,-1001,1287,-924,330,-45,1,1,-19,153,-680,1820,-3003,3003,-1716,495,-55,1
%N A076756 Triangle of coefficients of characteristic polynomial of M_n, the n X n matrix M_(i,j) = min(i,j).
%C A076756 The characteristic polynomial of M_n seems to be p(n,x) = (-1)^n * sum_{i=0..n} (-x)^i * binomial(2n-i, i). - _Enrique Pérez Herrero_, Jan 29 2013
%H A076756 Alois P. Heinz, <a href="/A076756/b076756.txt">Rows n = 0..140, flattened</a> (rows 0..60 from Enrique Pérez Herrero)
%H A076756 J. L. Jacobsen, and J. Salas, <a href="http://arxiv.org/abs/cond-mat/0407444">Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models IV. Chromatic polynomial with cyclic boundary conditions</a>, J. Stat. Phys. 122 (2006) 705-760, arXiv:cond-mat/0407444. See Eq. 2.27. - _N. J. A. Sloane_, Mar 14 2014
%e A076756 Triangle begins:
%e A076756    1;
%e A076756   -1,   1;
%e A076756    1,  -3,   1;
%e A076756   -1,   5,  -6,   1;
%e A076756    1,  -7,  15, -10,    1;
%e A076756   -1,   9, -28,  35,  -15,   1;
%e A076756    1, -11,  45, -84,   70, -21,   1;
%e A076756   -1,  13, -66, 165, -210, 126, -28,  1;
%p A076756 T:=(n, k)-> binomial(2*n-k, k)*(-1)^(n+k):
%p A076756 seq(seq(T(n, k), k=0..n), n=0..14);  # _Alois P. Heinz_, Feb 01 2013
%t A076756 T[n_, k_] := Binomial[2*n - k, k]*(-1)^(n + k); Table[Table[T[n, k], {k, 0, n}], {n, 0, 14}] // Flatten (* _Jean-François Alcover_, Jun 12 2015, after _Alois P. Heinz_ *)
%Y A076756 Absolute values are A054142.
%Y A076756 Cf. A203989.
%K A076756 sign,tabl
%O A076756 0,5
%A A076756 _Benoit Cloitre_, Nov 09 2002
%E A076756 Offset corrected by _Alois P. Heinz_, Feb 01 2013