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Triangle, read by rows, where T(0,0) = 1, T(n,k) = (-1)^n*(2n+1)*T(n-1,k) - T(n-1,k-1).
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%I #5 Apr 11 2013 08:16:06

%S 1,-3,-1,-15,-2,1,105,29,-5,-1,945,156,-74,-4,1,-10395,-2661,658,118,

%T -7,-1,-135135,-24198,11215,876,-209,-6,1,2027025,498105,-144027,

%U -24355,2259,299,-9,-1,34459425,6440760,-2946564,-270008,62758,2824,-452,-8,1,-654729075,-156833865,49543956,8076716

%N Triangle, read by rows, where T(0,0) = 1, T(n,k) = (-1)^n*(2n+1)*T(n-1,k) - T(n-1,k-1).

%C Row sums are (-1)^round(n/2) * 2^(2*n) * floor(n/2)! * round(n/2 + 1/2)!.

%e Triangle begins

%e 1;

%e -3, -1;

%e -15, -2, 1;

%e 105, 29, -5, -1;

%e 945, 156, -74, -4, 1;

%o (PARI) t(n, k) = {if (k < 0, return (0)); if (n < k, return (0)); if (n == 0, return (1)); return ((-1)^n*(2*n+1)*t(n-1,k) - t(n-1,k-1));} \\ _Michel Marcus_, Apr 11 2013

%K sign,tabl

%O 0,2

%A _Gerald McGarvey_, Jun 04 2005