A154556 - OEIS

%I #7 Jul 19 2019 14:26:55

%S 1,-1,1,1,-1,1,-1,0,0,1,1,2,-3,2,1,-1,-5,5,-5,5,1,1,9,0,-5,0,9,1,-1,

%T -14,-21,35,-35,21,14,1,1,20,70,-56,35,-56,70,20,1,-1,-27,-162,-42,

%U 189,-189,42,162,27,1

%N Exponential Riordan array [exp(-x), x(1+x/2)]

%C Row sums are double factorials A001147 (aerated).

%C Product A007318*(this triangle) is A122848.

%F T(n,k) = (n!/k!)*sum{j=0..k, (-1)^(n-k)*C(k,j)*(-1/2)^j/(n-k-j)!};

%F T(n,k) = sum{j=0..n, (-1)^(n-j)*C(n,j)*C(j,k)*k!/((2k-j)!*2^(j-k))};

%e Triangle begins

%e 1,

%e -1, 1,

%e 1, -1, 1,

%e -1, 0, 0, 1,

%e 1, 2, -3, 2, 1,

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

%e 1, 9, 0, -5, 0, 9, 1,

%e -1, -14, -21, 35, -35, 21, 14, 1,

%e 1, 20, 70, -56, 35, -56, 70, 20, 1,

%e -1, -27, -162, -42, 189, -189, 42, 162, 27, 1,

%e 1, 35, 315, 510, -735, 693, -735, 510, 315, 35, 1

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

%t RiordanArray[E^-#&, # (1 + #/2)&, 10, True] // Flatten (* _Jean-François Alcover_, Jul 19 2019 *)

%Y Cf. A001147, A007318, A122848.

%K easy,sign,tabl

%O 0,12

%A _Paul Barry_, Jan 11 2009