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

0,5

Comments

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

Links

Table of n, a(n) for n=0..44.

Formula

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

Example

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

Mathematica

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

Crossrefs

Cf. A122832.

Sequence in context: A106534 A123346 A163840 * A193692 A344028 A075303

Adjacent sequences: A122830 A122831 A122832 * A122834 A122835 A122836

Keyword

easy,sign,tabl

Author

Paul Barry, Sep 12 2006

Status

approved