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%I #15 Sep 03 2023 08:41:24
%S 1,1,-1,1,-2,0,1,-3,1,1,1,-4,3,2,0,1,-5,6,2,-2,-2,1,-6,10,0,-6,-4,0,1,
%T -7,15,-5,-11,-3,5,5,1,-8,21,-14,-15,4,15,10,0,1,-9,28,-28,-15,19,26,
%U 6,-14,-14,1,-10,36,-48,-7,42,30,-16,-42,-28,0,1,-11,45,-75,14,70,16,-60,-70,-14,42,42,1,-12,55,-110,54,96,-28,-120,-70,56,126,84,0
%N Triangle related to Catalan triangle: recurrence related to A033877 (Schroeder numbers).
%C Sums of odd rows are 0, of even rows are the Catalan numbers (A000108) with alternating signs. Row sums of unsigned version give A065441.
%e Triangle starts:
%e [0] 1;
%e [1] 1, -1;
%e [2] 1, -2, 0;
%e [3] 1, -3, 1, 1;
%e [4] 1, -4, 3, 2, 0;
%e [5] 1, -5, 6, 2, -2, -2;
%e [6] 1, -6, 10, 0, -6, -4, 0;
%e [7] 1, -7, 15, -5, -11, -3, 5, 5;
%e [8] 1, -8, 21, -14, -15, 4, 15, 10, 0;
%e [9] 1, -9, 28, -28, -15, 19, 26, 6, -14, -14.
%t a[0, 0] := 1; a[n_, k_] := 0/;(k > n||n < 0||k < 0); a[n_, k_] := a[n, k] = a[n, k-1]-2a[n-1, k-1]+a[n-1, k]; Table[a[n, k], {n, 0, 16}, {k, 0, n}]
%K sign,tabl
%O 0,5
%A _Wouter Meeussen_, Nov 16 2001
%E More terms from _Sean A. Irvine_, Sep 03 2023
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