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

1, 2, -2, -12, 126, -84, -10532, 72584, 1398454, -23934644, -279791836, 10005551128, 74538179116, -5628788533000, -20339727800264, 4187789575589776, -1855072071151834, -4010464443848609780

Offset

0,2

Comments

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

References

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

Links

Table of n, a(n) for n=0..17.

Formula

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

Prog

(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))

Crossrefs

Sequence in context: A032321 A013311 A303343 * A032320 A032227 A032069

Adjacent sequences: A087217 A087218 A087219 * A087221 A087222 A087223

Keyword

sign

Author

Michael Somos, Aug 27 2003

Status

approved