A122833 Exponential Riordan array (e^(-x(1+x)),x).

1, -1, 1, -1, -2, 1, 5, -3, -3, 1, 1, 20, -6, -4, 1, -41, 5, 50, -10, -5, 1, 31, -246, 15, 100, -15, -6, 1, 461, 217, -861, 35, 175, -21, -7, 1, -895, 3688, 868, -2296, 70, 280, -28, -8, 1

Offset: 0

Author

Paul Barry, Sep 12 2006

Keywords

• easy
• sign
• tabl

Comments

Inverse of A122832. Row sums are (-1)^(n/2)(1+(-1)^n)(n)!/(2(n/2)!).

Examples

			Triangle begins
1,
-1, 1,
-1, -2, 1,
5, -3, -3, 1,
1, 20, -6, -4, 1,
-41, 5, 50, -10, -5, 1
		

Crossrefs

Cf. A122832.

Programs

Mathematica

(* The function RiordanArray is defined in A256893. *)
RiordanArray[E^(-# (1 + #))&, #&, 9, True] // Flatten (* Jean-François Alcover, Jul 19 2019 *)

Formula

Number triangle T(n,k)=(n!/k!)sum{i=0..n-k, (-1)^i*C(i,n-k-i)/i!}