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%I
%S 1,1,3,31,301,571,51751,926731,3281851,479961901,13256384851,
%T 9729091003,13915350562081,74105896232383,3502203417248521,
%U 919071064063596151,43167975952565245501,361179801176946547051,16542165057245024351233,6561750899663711363984851
%N Numerators of expansion of exp(1-sqrt(1-x-x^2)).
%H Robert Israel, <a href="/A144579/b144579.txt">Table of n, a(n) for n = 0..377</a>
%F 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
%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(numer(g(n)),n=0..40); # _Robert Israel_, Dec 31 2019
%t CoefficientList[Series[Exp[1-Sqrt[1-x-x^2]],{x,0,20}],x]//Numerator (* _Harvey P. Dale_, Dec 26 2018 *)
%Y Cf. A144580.
%K nonn,frac
%O 0,3
%A _N. J. A. Sloane_, Jan 07 2009
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