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E.g.f.: x + (gdinv x - sinh x)/2, where gdinv = inverse-Gudermannian. Sequence has odd-indexed coefficients; others are zero.
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%I #16 Nov 13 2016 06:20:44

%S 1,0,2,30,692,25260,1351382,99680490,9695756072,1202439837720,

%T 185185594118762,34674437196568950,7757267081778543452,

%U 2043536254646561946180,626129820701814932734142,220771946624511552276841410

%N E.g.f.: x + (gdinv x - sinh x)/2, where gdinv = inverse-Gudermannian. Sequence has odd-indexed coefficients; others are zero.

%C Also gdinv(x) = log(tan(x) + sec(x)).

%H G. C. Greubel, <a href="/A013525/b013525.txt">Table of n, a(n) for n = 0..200</a>

%F For n>0, a(n) = (1/2) * (A000364(n) - 1).

%e x + (gdinv x - sinh x)/2 = x + 2/5!*x^5 + 30/7!*x^7 + 692/9!*x^9 + ...

%t With[{nn=40},Take[CoefficientList[Series[x+(InverseGudermannian[x]-Sinh[ x])/2,{x,0,nn}],x] Range[0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, Oct 16 2014 *)

%K nonn,easy

%O 0,3

%A Patrick Demichel (patrick.demichel(AT)hp.com)

%E Definition corrected by _Ralf Stephan_ and _Don Reble_, Dec 16 2004