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

%I A166358 #13 Jul 20 2019 08:03:13
%S A166358 1,1,3,7,21,61,295,1331,10409,65017,694411,5454879,73145149,689074101,
%T A166358 11090013103,121652191051,2282132463953,28550033871857,
%U A166358 611369381873683,8587415858721079,206626962757626981,3219065122124476717
%N A166358 Row sums of exponential Riordan array [1+x*arctanh(x), x], A166357.
%C A166358 Binomial transform of aeration of A166356.
%F A166358 E.g.f.: exp(x)*(1+x*arctanh(x)).
%F A166358 a(n) = Sum_{k=0..n} C(n,k)*A166356(k/2)*(1+(-1)^k)/2.
%F A166358 a(n) ~ (exp(1) + (-1)^n*exp(-1)) * (n-1)! / 2. - _Vaclav Kotesovec_, Aug 17 2018
%t A166358 (* The function RiordanArray is defined in A256893. *)
%t A166358 nmax = 21; R = RiordanArray[1 + # ArcTanh[#]&, #&, nmax + 1, True];
%t A166358 Total /@ R (* _Jean-François Alcover_, Jul 20 2019 *)
%Y A166358 Cf. A166356, A166357.
%K A166358 easy,nonn
%O A166358 0,3
%A A166358 _Paul Barry_, Oct 12 2009