cp's OEIS Frontend

A166353 Exponential Riordan array [1+x*tan(x/2),x].

%I A166353 #7 Jul 19 2019 14:27:13
%S A166353 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 A166353 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 A166353 0,630,0,210,0,45,0,1
%N A166353 Exponential Riordan array [1+x*tan(x/2),x].
%C A166353 First column is aerated Genocchi number variant with e.g.f. 1+x*tan(x/2).
%C A166353 Row sums are A166354. Diagonal sums are A166355.
%F A166353 T(n,k) = [k<=n]*G((n-k)/2)*C(n,k)*(1+(-1)^(n-k))/2 where
%F A166353 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 A166353 Triangle begins
%e A166353 1,
%e A166353 0, 1,
%e A166353 1, 0, 1,
%e A166353 0, 3, 0, 1,
%e A166353 1, 0, 6, 0, 1,
%e A166353 0, 5, 0, 10, 0, 1,
%e A166353 3, 0, 15, 0, 15, 0, 1,
%e A166353 0, 21, 0, 35, 0, 21, 0, 1,
%e A166353 17, 0, 84, 0, 70, 0, 28, 0, 1,
%e A166353 0, 153, 0, 252, 0, 126, 0, 36, 0, 1,
%e A166353 155, 0, 765, 0, 630, 0, 210, 0, 45, 0, 1
%t A166353 (* The function RiordanArray is defined in A256893. *)
%t A166353 RiordanArray[1 + # Tan[#/2]&, #&, 11, True] // Flatten (* _Jean-François Alcover_, Jul 19 2019 *)
%Y A166353 Cf. A110501, A166354, A166355.
%K A166353 easy,nonn,tabl
%O A166353 0,8
%A A166353 _Paul Barry_, Oct 12 2009