%I #9 Mar 29 2016 03:41:23
%S 1,0,-1,0,-1,1,0,-2,1,2,-1,0,-5,5,-1,5,-2,-3,1,0,-14,21,-3,-6,1,14,
%T -12,2,-9,3,4,-1,0,-42,84,-28,-28,7,7,-1,42,-56,7,14,-2,-28,21,-3,14,
%U -4,-5,1
%N Triangle read by rows, the coefficients of the inverse partial P-polynomials.
%C The triangle of coefficients of the partial P-polynomials is A269941. For the definition of the inverse partial P-polynomials see the link 'P-transform'.
%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/P-Transform">The P-transform</a>.
%e [[1]],
%e [[0], [-1]],
%e [[0], [-1], [1]],
%e [[0], [-2, 1], [2], [-1]],
%e [[0], [-5, 5, -1], [5, -2], [-3], [1]],
%e [[0], [-14, 21, -3, -6, 1], [14, -12, 2], [-9, 3], [4], [-1]]],
%e [[0], [-42,84,-28,-28,7,7,-1],[42,-56,7,14,-2],[-28,21,-3],[14,-4],[-5],[1]]
%e Replacing the sublists by their sums reduces the triangle to a signed version of the triangle A097805. The column 1 of sublists is A111785 in a different order.
%o (Sage)
%o # For function PMultiCoefficients see A269941.
%o PMultiCoefficients(7, inverse = True)
%Y Cf. A097805, A111785, A268441, A268442, A269941.
%K sign,tabf
%O 0,8
%A _Peter Luschny_, Mar 08 2016