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Search: id:A087216
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| 1, 30, 6930, 3063060, 2007835830, 1746817172100, 1895296631728500, 2464427134570401000, 3735455429225085315750, 6467318499798364376668500, 12591869119107415441373569500, 27232778758505946668207019855000
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OFFSET
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0,2
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COMMENT
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G.f. A(x) yields asymptotic expansion of Airy function Ai(x) ~ f((2/3)x^(3/2))/(2sqrt(pi)x^(1/4)) where f(x)=A(-1/(432x))/exp(x).
G.f. A(x) yields asymptotic expansion of Airy function Bi(x) ~ f((2/3)x^(3/2))/(sqrt(pi)x^(1/4)) where f(x)=A(1/(432x))*exp(x).
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REFERENCES
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R. P. Stanley, Recent Progress in Algebraic Combinatorics, Bull. Amer. Math. Soc., 40 (2003), 55-68.
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 448.
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LINKS
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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].
F. W. J. Olver, Link to a section of the Digital Library of Mathematical Functions.
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FORMULA
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G.f. A(x) satisfies 216x^2A(x)''+(432x-1)A(x)'+30A(x)=0.
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PROGRAM
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(PARI) a(n)=if(n<0, 0, (6*n)!/(3*n)!/(2*n)!/2^n)
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CROSSREFS
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Sequence in context: A115465 A127849 A050984 this_sequence A059049 A056071 A137749
Adjacent sequences: A087213 A087214 A087215 this_sequence A087217 A087218 A087219
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Aug 26 2003
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