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Eexpansion of e.g.f. exp(arcsinh(x)*arcsin(x)).
2

%I #10 Dec 10 2024 05:38:39

%S 1,2,12,208,6608,438912,38672832,5956592640,1035058952448,

%T 288405058560000,83042522104507392,36519438671549890560,

%U 15719007594987094364160,10017433660808198506414080

%N Eexpansion of e.g.f. exp(arcsinh(x)*arcsin(x)).

%H Harvey P. Dale, <a href="/A012598/b012598.txt">Table of n, a(n) for n = 0..200</a>

%e 1+2/2!*x^2+12/4!*x^4+208/6!*x^6+6608/8!*x^8...

%t With[{nn=30},Take[CoefficientList[Series[Exp[ArcSinh[x]ArcSin[x]],{x,0,nn}], x]Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, May 19 2012 *)

%K nonn

%O 0,2

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

%E Definition clarified by _Harvey P. Dale_, May 19 2012