A012316 - OEIS

%I #13 Sep 08 2022 08:44:38

%S 1,1,3,11,49,265,1635,11531,90241,785777,7464483,77615947,870363377,

%T 10565245561,137126790723,1910729723787,28271549169025,

%U 446132922949985,7432565149802947,131334851550591627

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

%H G. C. Greubel, <a href="/A012316/b012316.txt">Table of n, a(n) for n = 0..449</a>

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

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

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

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(asin(x)*exp(x)))) \\ _G. C. Greubel_, Oct 25 2018

%o (Magma) m:=30; R<x>:=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

%K nonn

%O 0,3

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

%E Definition clarified by _Harvey P. Dale_, Jul 31 2014