%I #7 Jul 19 2019 14:27:13

%S 1,0,1,1,0,1,0,3,0,1,1,0,6,0,1,0,5,0,10,0,1,3,0,15,0,15,0,1,0,21,0,35,

%T 0,21,0,1,17,0,84,0,70,0,28,0,1,0,153,0,252,0,126,0,36,0,1,155,0,765,

%U 0,630,0,210,0,45,0,1

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

%C First column is aerated Genocchi number variant with e.g.f. 1+x*tan(x/2).

%C Row sums are A166354. Diagonal sums are A166355.

%F T(n,k) = [k<=n]*G((n-k)/2)*C(n,k)*(1+(-1)^(n-k))/2 where

%F G(n)=0^n+2(-1)^n*(1-4^n)*sum{k=0..2n, sum{j=0..k, (-1)^j*C(k,j)*j^(2n)/(k+1)}}.

%e Triangle begins

%e 1,

%e 0, 1,

%e 1, 0, 1,

%e 0, 3, 0, 1,

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

%e 0, 5, 0, 10, 0, 1,

%e 3, 0, 15, 0, 15, 0, 1,

%e 0, 21, 0, 35, 0, 21, 0, 1,

%e 17, 0, 84, 0, 70, 0, 28, 0, 1,

%e 0, 153, 0, 252, 0, 126, 0, 36, 0, 1,

%e 155, 0, 765, 0, 630, 0, 210, 0, 45, 0, 1

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

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

%Y Cf. A110501, A166354, A166355.

%K easy,nonn,tabl

%O 0,8

%A _Paul Barry_, Oct 12 2009