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%I #16 Nov 02 2020 11:07:05
%S 1,1,1,1,1,9,49,225,897,11025,96801,893025,6803457,108056025,
%T 1275363153,18261468225,207592347393,4108830350625,60889593787713,
%U 1187451971330625,17888210916886017,428670161650355625,7679611833095218545,189043541287806830625,3530100224793651058305
%N Expansion of e.g.f. exp(arcsinh(arcsin(x))).
%F E.g.f.: Q(0)-1, where Q(k) = 2 + arcsin(x)/(1 - arcsin(x)/Q(k+1) ); (continued fraction). - _Sergei N. Gladkovskii_, Dec 19 2013
%e 1 + x + 1/2!*x^2 + 1/3!*x^3 + 1/4!*x^4 + 9/5!*x^5...
%t With[{nn=25},CoefficientList[Series[Exp[ArcSinh[ArcSin[x]]],{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Nov 02 2020 *)
%o (PARI) x = 'x + O('x^30); Vec(serlaplace(exp(asinh(asin(x))))) \\ _Michel Marcus_, Mar 09 2017
%Y Bisections are |A012115(n)| and A001818.
%K nonn
%O 0,6
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E More terms from _Michel Marcus_, Mar 09 2017
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