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

%I #7 Jul 19 2019 14:22:41

%S 1,-1,1,-1,-2,1,5,-3,-3,1,1,20,-6,-4,1,-41,5,50,-10,-5,1,31,-246,15,

%T 100,-15,-6,1,461,217,-861,35,175,-21,-7,1,-895,3688,868,-2296,70,280,

%U -28,-8,1

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

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

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

%e Triangle begins

%e 1,

%e -1, 1,

%e -1, -2, 1,

%e 5, -3, -3, 1,

%e 1, 20, -6, -4, 1,

%e -41, 5, 50, -10, -5, 1

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

%t RiordanArray[E^(-# (1 + #))&, #&, 9, True] // Flatten (* _Jean-François Alcover_, Jul 19 2019 *)

%Y Cf. A122832.

%K easy,sign,tabl

%O 0,5

%A _Paul Barry_, Sep 12 2006