login
Exponential Riordan array [1+x^2*sec(x), x].
1

%I #5 Jul 19 2019 14:25:54

%S 1,0,1,2,0,1,0,6,0,1,12,0,12,0,1,0,60,0,20,0,1,150,0,180,0,30,0,1,0,

%T 1050,0,420,0,42,0,1,3416,0,4200,0,840,0,56,0,1,0,30744,0,12600,0,

%U 1512,0,72,0,1,124650,0,153720,0,31500,0,2520,0,90,0,1

%N Exponential Riordan array [1+x^2*sec(x), x].

%C Row sums are A166379. Diagonal sums are A166380.

%F Number triangle T(n,k)=[k<=n]*A166377((n-k)/2)*C(n,k)*(1+(-1)^(n-k))/2.

%e Triangle begins

%e 1,

%e 0, 1,

%e 2, 0, 1,

%e 0, 6, 0, 1,

%e 12, 0, 12, 0, 1,

%e 0, 60, 0, 20, 0, 1,

%e 150, 0, 180, 0, 30, 0, 1,

%e 0, 1050, 0, 420, 0, 42, 0, 1,

%e 3416, 0, 4200, 0, 840, 0, 56, 0, 1,

%e 0, 30744, 0, 12600, 0, 1512, 0, 72, 0, 1,

%e 124650, 0, 153720, 0, 31500, 0, 2520, 0, 90, 0, 1

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

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

%K easy,nonn,tabl

%O 0,4

%A _Paul Barry_, Oct 13 2009