%I #11 Jul 20 2019 08:02:58

%S 1,0,1,-2,0,1,0,-6,0,1,12,0,-12,0,1,0,60,0,-20,0,1,-120,0,180,0,-30,0,

%T 1,0,-840,0,420,0,-42,0,1,1680,0,-3360,0,840,0,-56,0,1,0,15120,0,

%U -10080,0,1512,0,-72,0,1,-30240,0,75600,0,-25200,0,2520,0,-90,0,1,0,-332640,0,277200,0,-55440,0,3960,0,-110,0,1,665280,0

%N A scaled Hermite triangle.

%C Inverse of number triangle A067147. Diagonal sums are A002119.

%H <a href="/index/He#Hermite">Index entries for sequences related to Hermite polynomials</a>

%F Number triangle T(n, k)=A060821(n, k)/2^k; T(n, k)=n!/(k!*2^((n-k)/2)((n-k)/2)!)*cos(pi*(n-k)/2)*2^((n+k)/2)(1+(-1)^(n+k))/2^(k+1) T(n, k)=A001498((n+k)/2, (n-k)/2)*cos(pi(n-k)/2)*2^((n+k)/2)(1+(-1)^(n+k))/2^(k+1);

%F Exponential Riordan array (e^(-x^2),x). - _Paul Barry_, Sep 12 2006

%e Triangle begins

%e 1;

%e 0,1;

%e -2,0,1;

%e 0,-6,0,1;

%e 12,0,-12,0,1;

%e 0,60,0,-20,0,1;

%t (* The function RiordanArray is defined in A256893. *)

%t rows = 12;

%t R = RiordanArray[E^(-#^2)&, #&, rows, True];

%t R // Flatten

%K easy,sign,tabl

%O 0,4

%A _Paul Barry_, Aug 28 2005