|
%I #14 May 09 2023 13:34:28
%S 1,2,4,48,384,640,46080,645120,1720320,185794560,3715891200,
%T 1946419200,1961990553600,7287393484800,238054853836800,
%U 42849873690624000,1371195958099968000,7770110429233152000,239763407530622976000,63777066403145711616000
%N Denominators of expansion of exp(1-sqrt(1-x-x^2)).
%C D-finite with recurrence: Expansion satisfies 8*a(n)+12*a(n+1)+(22+8*n^2+24*n)*a(n+2)+(73+12*n^2+60*n)*a(n+3)+(-18*n-8-4*n^2)*a(n+4)+(-4*n^2-36*n-80)*a(n+5)=0. - _Robert Israel_, Dec 31 2019
%H Robert Israel, <a href="/A144580/b144580.txt">Table of n, a(n) for n = 0..403</a>
%e The expansion is 1 + (1/2)*x + (3/4)*x^2 + (31/48)*x^3 + (301/384)*x^4 + (571/640)*x^5 + (51751/46080)*x^6 + ( 926731/645120)*x^7 + (3281851/1720320)*x^8 + ...
%p g:= gfun:-rectoproc({8*a(n)+12*a(n+1)+(22+8*n^2+24*n)*a(n+2)+(73+12*n^2+60*n)*a(n+3)+(-18*n-8-4*n^2)*a(n+4)+(-4*n^2-36*n-80)*a(n+5), a(0) = 1, a(1) = 1/2, a(2) = 3/4, a(3) = 31/48, a(4) = 301/384}, a(n), remember):
%p seq(denom(g(n)), n=0..40); # Robert Israel, Dec 31 2019
%t CoefficientList[Series[Exp[1-Sqrt[1-x-x^2]],{x,0,20}],x]//Denominator (* _Harvey P. Dale_, May 09 2023 *)
%Y Cf. A144579.
%K nonn,frac
%O 0,2
%A _N. J. A. Sloane_, Jan 07 2009
|
