A166358 Row sums of exponential Riordan array [1+x*arctanh(x), x], A166357.

1, 1, 3, 7, 21, 61, 295, 1331, 10409, 65017, 694411, 5454879, 73145149, 689074101, 11090013103, 121652191051, 2282132463953, 28550033871857, 611369381873683, 8587415858721079, 206626962757626981, 3219065122124476717

Offset: 0

Author

Paul Barry, Oct 12 2009

Keywords

• easy
• nonn

Comments

Binomial transform of aeration of A166356.

Crossrefs

Cf. A166356, A166357.

Programs

Mathematica

(* The function RiordanArray is defined in A256893. *)
nmax = 21; R = RiordanArray[1 + # ArcTanh[#]&, #&, nmax + 1, True];
Total /@ R (* Jean-François Alcover, Jul 20 2019 *)

Formula

E.g.f.: exp(x)*(1+x*arctanh(x)).

a(n) = Sum_{k=0..n} C(n,k)*A166356(k/2)*(1+(-1)^k)/2.

a(n) ~ (exp(1) + (-1)^n*exp(-1)) * (n-1)! / 2. - Vaclav Kotesovec, Aug 17 2018