0,2

The series arises in the asymptotic expansion of the Airy function A(x) for large |x| as Ai(x)~pi^(-1/2)/2*x^(-1/4)*exp(-z)*sum((-1)^k*c(k)*z^(-k),k=0..infinity), where z=2/3*x^(3/2). a(k) is the denominator of the fully canceled c(k).

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings).

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].

NIST's Digital Library of Mathematical Functions, Airy and Related Functions (Poincare-Type Expansions) by Frank W. J. Olver.

a(k)=denom(product((2*l+1), l=k..3*k-1)/216^k/k!)

a(2)=2592 because for k=2, product((2*l+1),l=k..3*k-1)/216^k/k! = 3465/23328 = 385/2592, and we take the denominator of the fully canceled fraction.

Michael Somos points out that that example is wrong, a(2) is not 2592. Aug 29 2004

Cf. A060506, A014402, A014403.

Sequence in context: A093272 A105347 A093236 this_sequence A048544 A062076 A008703

Adjacent sequences: A060504 A060505 A060506 this_sequence A060508 A060509 A060510

easy,frac,nonn

Michael Praehofer (praehofer(AT)ma.tum.de), Mar 22 2001