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A138057 Triangle read by rows: row n consists of 0 followed by n (n+1)'s with alternating signs.

%I A138057 #11 Nov 10 2023 03:44:49
%S A138057 0,0,-2,0,-3,3,0,-4,4,-4,0,-5,5,-5,5,0,-6,6,-6,6,-6,0,-7,7,-7,7,-7,7,
%T A138057 0,-8,8,-8,8,-8,8,-8,0,-9,9,-9,9,-9,9,-9,9,0,-10,10,-10,10,-10,10,-10,
%U A138057 10,-10
%N A138057 Triangle read by rows: row n consists of 0 followed by n (n+1)'s with alternating signs.
%H A138057 Paolo Xausa, <a href="/A138057/b138057.txt">Table of n, a(n) for n = 0..1325</a> (rows 0..50 of the triangle, flattened).
%F A138057 T(n,k) = [k>0]*(n+1)*(-1)^k, with n >= 0 and 0 <= k <= n, where [] is the Iverson bracket. - _Paolo Xausa_, Nov 10 2023
%e A138057 From _Paolo Xausa_, Nov 10 2023: (Start)
%e A138057 Triangle begins:
%e A138057   n\k|  0   1   2   3   4  ...
%e A138057   ---+---------------------
%e A138057    0 |  0;
%e A138057    1 |  0, -2;
%e A138057    2 |  0, -3,  3;
%e A138057    3 |  0, -4,  4, -4;
%e A138057    4 |  0, -5,  5, -5,  5;
%e A138057   ... (End)
%t A138057 Array[Join[{0},(-1)^Range[#](#+1)]&,15,0] (* _Paolo Xausa_, Nov 10 2023 *)
%Y A138057 Cf. A131738.
%K A138057 tabl,sign
%O A138057 0,3
%A A138057 _Paul Curtz_, May 02 2008