A166380 Diagonal sums of exponential Riordan array [1+x^2*sec(x),x], A166378.

1, 3, 19, 223, 4667, 160045, 8207125, 587420875, 55869454855, 6809387511403, 1034264079708019, 191477762192490649, 42435372869814513769, 11090351278621719882899, 3374951549996881393302715

Offset: 0

Author

Paul Barry, Oct 13 2009

Keywords

• easy
• nonn

Crossrefs

Cf. A166377, A166378.

Programs

Mathematica

(* The function RiordanArray is defined in A256893. *)
nmax = 14; R = RiordanArray[1 + #^2  Sec[#]&, #&, 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)*A166377(k).