A129684 Exponential Riordan array [1/(1-x^2/2), x].
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, 210, 0, 21, 0, 1, 2520, 0, 2520, 0, 420, 0, 28, 0, 1, 0, 22680, 0, 7560, 0, 756, 0, 36, 0, 1, 113400, 0, 113400, 0, 18900, 0, 1260, 0, 45, 0, 1
Offset: 0
Examples
Triangle begins 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, 210, 0, 21, 0, 1
Programs
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Mathematica
(* The function RiordanArray is defined in A256893. *) RiordanArray[1/(1 - #^2/2)&, #&, 11, True] // Flatten (* Jean-François Alcover, Jul 19 2019 *)
Formula
Number triangle T(n,k) = [k<=n](n!/k!)*(1/2^((n-k)/2))*(1+(-1)^(n-k))/2.
Comments