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%I #14 Oct 17 2014 23:54:25
%S 1,-1,1,3,-3,1,-5,9,-5,1,11,-23,19,-7,1,-21,57,-61,33,-9,1,43,-135,
%T 179,-127,51,-11,1,-85,313,-493,433,-229,73,-13,1,171,-711,1299,-1359,
%U 891,-375,99,-15,1,-341,1593,-3309,4017,-3141,1641,-573,129,-17,1,683,-3527,8211,-11343,10299,-6423,2787,-831,163,-19,1
%N Signed version of A164984.
%C Consider the transformation 1 + x + x^2 + x^3 + ... + x^n = A_0*(x+2)^0 + A_1*(x+2)^1 + A_2*(x+2)^2 + ... + A_n*(x+2)^n. This sequence gives A_0, ... A_n as the entries in the n-th row of this triangle, starting at n = 0.
%F T(n,n-1) = -2*n+1 for n > 0.
%F T(n,n-2) = 2*(n-1)^2+1 for n > 1.
%F T(n,0) = A077925(n).
%F T(n,1) = (-1)^(n+1)*A045883(n).
%F Rows with odd n sum to 0.
%F Rows with even n sum to 1.
%e 1;
%e -1, 1;
%e 3, -3, 1;
%e -5, 9, -5, 1;
%e 11, -23, 19, -7, 1;
%e -21, 57, -61, 33, -9, 1;
%e 43, -135, 179, -127, 51, -11, 1;
%e -85, 313, -493, 433, -229, 73, -13, 1;
%e 171, -711, 1299, -1359, 891, -375, 99, -15, 1;
%e -341, 1593, -3309, 4017, -3141, 1641, -573, 129, -17, 1;
%e 683, -3527, 8211, -11343, 10299, -6423, 2787, -831, 163, -19, 1;
%o (PARI) for(n=0,20,for(k=0,n,print1(1/k!*sum(i=0,n,((-2)^(i-k)*prod(j=0,k-1,i-j))),", ")))
%Y Cf. A164984, A193845, A077925, A045883.
%K sign,tabl
%O 0,4
%A _Derek Orr_, Oct 14 2014