A259647 Expansion of exp(x*arcsin(x)) (even powers only).

1, 2, 16, 294, 10424, 635130, 60535212, 8378845734, 1591416365520, 397329777218034, 126160335768212820, 49635257475383554590, 23694522124288261524984, 13490127107426613875639850, 9029074877857980800375629500, 7018229497764789751949369835030

Offset: 0

Author

Vaclav Kotesovec, Jul 02 2015

Keywords

• nonn

Crossrefs

Cf. A006228, A191301.

Programs

Mathematica

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

Formula

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