A112227 A scaled Hermite triangle.

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

Offset: 0

Author

Paul Barry, Aug 28 2005

Keywords

• easy
• sign
• tabl

Comments

Inverse of number triangle A067147. Diagonal sums are A002119.

Examples

			Triangle begins
1;
0,1;
-2,0,1;
0,-6,0,1;
12,0,-12,0,1;
0,60,0,-20,0,1;
		

Links

• Index entries for sequences related to Hermite polynomials

Programs

Mathematica

(* The function RiordanArray is defined in A256893. *)
rows = 12;
R = RiordanArray[E^(-#^2)&, #&, rows, True];
R // Flatten

Formula

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);

Exponential Riordan array (e^(-x^2),x). - Paul Barry, Sep 12 2006