A129684 - OEIS

%I #7 Jul 19 2019 14:26:39

%S 1,0,1,1,0,1,0,3,0,1,6,0,6,0,1,0,30,0,10,0,1,90,0,90,0,15,0,1,0,630,0,

%T 210,0,21,0,1,2520,0,2520,0,420,0,28,0,1,0,22680,0,7560,0,756,0,36,0,

%U 1,113400,0,113400,0,18900,0,1260,0,45,0,1

%N Exponential Riordan array [1/(1-x^2/2), x].

%C Row sums are A087214. Inverse is A129685.

%F Number triangle T(n,k) = [k<=n](n!/k!)*(1/2^((n-k)/2))*(1+(-1)^(n-k))/2.

%e Triangle begins

%e 1,

%e 0, 1,

%e 1, 0, 1,

%e 0, 3, 0, 1,

%e 6, 0, 6, 0, 1,

%e 0, 30, 0, 10, 0, 1,

%e 90, 0, 90, 0, 15, 0, 1,

%e 0, 630, 0, 210, 0, 21, 0, 1

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

%t RiordanArray[1/(1 - #^2/2)&, #&, 11, True] // Flatten (* _Jean-François Alcover_, Jul 19 2019 *)

%Y Cf. A087214, A129685.

%K easy,nonn,tabl

%O 0,8

%A _Paul Barry_, Apr 28 2007