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Expansion of exp(x*arcsin(x)) (even powers only).
3

%I #5 Jul 02 2015 13:56:40

%S 1,2,16,294,10424,635130,60535212,8378845734,1591416365520,

%T 397329777218034,126160335768212820,49635257475383554590,

%U 23694522124288261524984,13490127107426613875639850,9029074877857980800375629500,7018229497764789751949369835030

%N Expansion of exp(x*arcsin(x)) (even powers only).

%F a(n) ~ (2*n)! * exp(Pi/2) / (2*sqrt(Pi)*n^(3/2)).

%t nmax=20; Table[(CoefficientList[Series[E^(x*ArcSin[x]), {x, 0, 2*nmax}], x] * Range[0, 2*nmax]!)[[2*n+1]], {n,0,nmax}]

%Y Cf. A006228, A191301.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Jul 02 2015