cp's OEIS Frontend

A248810 Signed version of A164984.

%I A248810 #14 Oct 17 2014 23:54:25
%S A248810 1,-1,1,3,-3,1,-5,9,-5,1,11,-23,19,-7,1,-21,57,-61,33,-9,1,43,-135,
%T A248810 179,-127,51,-11,1,-85,313,-493,433,-229,73,-13,1,171,-711,1299,-1359,
%U A248810 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 A248810 Signed version of A164984.
%C A248810 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 A248810 T(n,n-1) = -2*n+1 for n > 0.
%F A248810 T(n,n-2) = 2*(n-1)^2+1 for n > 1.
%F A248810 T(n,0) = A077925(n).
%F A248810 T(n,1) = (-1)^(n+1)*A045883(n).
%F A248810 Rows with odd n sum to 0.
%F A248810 Rows with even n sum to 1.
%e A248810 1;
%e A248810 -1,      1;
%e A248810 3,      -3,     1;
%e A248810 -5,      9,    -5,      1;
%e A248810 11,    -23,    19,     -7,     1;
%e A248810 -21,    57,   -61,     33,    -9,     1;
%e A248810 43,   -135,   179,   -127,    51,   -11,    1;
%e A248810 -85,   313,  -493,    433,  -229,    73,  -13,    1;
%e A248810 171,  -711,  1299,  -1359,   891,  -375,   99,  -15,   1;
%e A248810 -341, 1593, -3309,   4017, -3141,  1641, -573,  129, -17,   1;
%e A248810 683, -3527,  8211, -11343, 10299, -6423, 2787, -831, 163, -19, 1;
%o A248810 (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 A248810 Cf. A164984, A193845, A077925, A045883.
%K A248810 sign,tabl
%O A248810 0,4
%A A248810 _Derek Orr_, Oct 14 2014