Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #8 Jul 20 2019 08:03:06
%S 1,2,5,15,64,443,4887,78996,1745995,50333929,1829758158,81753825477,
%T 4399497764477,280491321580150,20898005984605281,1798558057748753171,
%U 177034863818072607020,19758697171102806823327
%N Diagonal sums of exponential Riordan array [1+x*tan(x/2),x], A166353.
%C Aerated sequence gives diagonal sums of A166353.
%F 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 (* The function RiordanArray is defined in A256893. *)
%t nmax = 17; R = RiordanArray[1 + # Tan[#/2]&, #&, 2 nmax + 1, True];
%t a[n_] := Sum[R[[i, 2 n - i + 2]], {i, 2 n + 1, n + 1, -1}];
%t Table[a[n], {n, 0, nmax}] (* _Jean-François Alcover_, Jul 20 2019 *)
%Y Cf. A110501, A166353.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Oct 12 2009