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A166355 Diagonal sums of exponential Riordan array [1+x*tan(x/2),x], A166353.

%I A166355 #8 Jul 20 2019 08:03:06
%S A166355 1,2,5,15,64,443,4887,78996,1745995,50333929,1829758158,81753825477,
%T A166355 4399497764477,280491321580150,20898005984605281,1798558057748753171,
%U A166355 177034863818072607020,19758697171102806823327
%N A166355 Diagonal sums of exponential Riordan array [1+x*tan(x/2),x], A166353.
%C A166355 Aerated sequence gives diagonal sums of A166353.
%F A166355 a(n)=sum{k=0..n, C(n+k,2k)*G(k)} where 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)}}.
%t A166355 (* The function RiordanArray is defined in A256893. *)
%t A166355 nmax = 17; R = RiordanArray[1 + # Tan[#/2]&, #&, 2 nmax + 1, True];
%t A166355 a[n_] := Sum[R[[i, 2 n - i + 2]], {i, 2 n + 1, n + 1, -1}];
%t A166355 Table[a[n], {n, 0, nmax}] (* _Jean-François Alcover_, Jul 20 2019 *)
%Y A166355 Cf. A110501, A166353.
%K A166355 easy,nonn
%O A166355 0,2
%A A166355 _Paul Barry_, Oct 12 2009