A012316 Expansion of e.g.f.: exp(arcsin(x)*exp(x)).

1, 1, 3, 11, 49, 265, 1635, 11531, 90241, 785777, 7464483, 77615947, 870363377, 10565245561, 137126790723, 1910729723787, 28271549169025, 446132922949985, 7432565149802947, 131334851550591627

Offset: 0

Author

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

Keywords

• nonn

Examples

			E.g.f. = 1+x+3/2!*x^2+11/3!*x^3+49/4!*x^4+265/5!*x^5...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..449

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(Arcsin(x)*Exp(x)))); [Factorial(n-1)*b[n]: n in [1..m-1]]; // G. C. Greubel, Oct 25 2018

Maple

seq(coeff(series(factorial(n)*exp(arcsin(x)*exp(x)),x,n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 25 2018

Mathematica

With[{nn=20},CoefficientList[Series[Exp[ArcSin[x]Exp[x]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jul 31 2014 *)

PARI

x='x+O('x^30); Vec(serlaplace(exp(asin(x)*exp(x)))) \\ G. C. Greubel, Oct 25 2018

Extensions

Definition clarified by Harvey P. Dale, Jul 31 2014