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A087220 Coefficients in an asymptotic series expanded in powers of 1/(4x). 0

%I

%S 1,2,-2,-12,126,-84,-10532,72584,1398454,-23934644,-279791836,

%T 10005551128,74538179116,-5628788533000,-20339727800264,

%U 4187789575589776,-1855072071151834,-4010464443848609780

%N Coefficients in an asymptotic series expanded in powers of 1/(4x).

%C G.f. yields asymptotic expansion of solutions to y''+(1+1/x)y=0.

%D N. G. de Bruijn, Asymptotic Methods in Analysis, Dover, 1981, p. 197.

%F G.f. A(x)=y satisfies 16x^3y*y'+8x^4y*y''+y^4-12x^4y'^2-(1+4x)y^2=0.

%o (PARI) a(n)=local(A, A1); if(n<0,0,A=1+2*x+O(x^2); for(k=1,n\2, A1=x^2*A'; A=sqrt((1+4*x)/(1+(8*x^2*A1'*A-12*A1^2)/A^4))); polcoeff(A,n))

%K sign

%O 0,2

%A _Michael Somos_, Aug 27 2003

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Last modified January 28 23:12 EST 2022. Contains 350670 sequences. (Running on oeis4.)