A012293 - OEIS

%I #12 Sep 08 2022 08:44:38

%S 1,0,1,6,25,140,1177,10738,104977,1188120,15191889,211088350,

%T 3187087209,52357837220,926871127977,17553084005322,354581844112801,

%U 7614153761167920,173108509344647457,4153655608324341686

%N Expansion of e.g.f. sec(sin(x)*exp(x))=1+1/2!*x^2+6/3!*x^3+25/4!*x^4+140/5!*x^5...

%H G. C. Greubel, <a href="/A012293/b012293.txt">Table of n, a(n) for n = 0..432</a>

%e E.g.f. = 1 + x^2/2! + 6*x^3/3! + 25*x^4/4! + 140*x^5/5! + ...

%t With[{nn=20},CoefficientList[Series[Sec[Sin[x]Exp[x]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jan 14 2012 *)

%o (PARI) x='x+O('x^30); Vec(serlaplace(1/cos(sin(x)*exp(x)))) \\ _G. C. Greubel_, Oct 26 2018

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( 1/Cos(Sin(x)*Exp(x)) )); [Factorial(n-1)*b[n]: n in [1..m-1]]; // _G. C. Greubel_, Oct 26 2018

%K nonn

%O 0,4

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