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A087220 Coefficients in an asymptotic series expanded in powers of 1/(4x). 0
1, 2, -2, -12, 126, -84, -10532, 72584, 1398454, -23934644, -279791836, 10005551128, 74538179116, -5628788533000, -20339727800264, 4187789575589776, -1855072071151834, -4010464443848609780 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 28 06:42 EST 2021. Contains 349401 sequences. (Running on oeis4.)