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

0,2

Links

Table of n, a(n) for n=0..15.

Formula

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

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}]

Crossrefs

Cf. A006228, A191301.

Sequence in context: A189611 A189689 A188740 * A188985 A362734 A009250

Adjacent sequences: A259644 A259645 A259646 * A259648 A259649 A259650

Keyword

nonn

Author

Vaclav Kotesovec, Jul 02 2015

Status

approved