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

1, 2, 5, 15, 64, 443, 4887, 78996, 1745995, 50333929, 1829758158, 81753825477, 4399497764477, 280491321580150, 20898005984605281, 1798558057748753171, 177034863818072607020, 19758697171102806823327

Offset: 0

Author

Paul Barry, Oct 12 2009

Keywords

• easy
• nonn

Comments

Aerated sequence gives diagonal sums of A166353.

Crossrefs

Cf. A110501, A166353.

Programs

Mathematica

(* The function RiordanArray is defined in A256893. *)
nmax = 17; R = RiordanArray[1 + # Tan[#/2]&, #&, 2 nmax + 1, True];
a[n_] := Sum[R[[i, 2 n - i + 2]], {i, 2 n + 1, n + 1, -1}];
Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Jul 20 2019 *)

Formula

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)}}.