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A087216 (6n)!/((3n)!(2n)!2^n). +0
1
1, 30, 6930, 3063060, 2007835830, 1746817172100, 1895296631728500, 2464427134570401000, 3735455429225085315750, 6467318499798364376668500, 12591869119107415441373569500, 27232778758505946668207019855000 (list; graph; listen)
OFFSET

0,2

COMMENT

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).

REFERENCES

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.

LINKS

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

F. W. J. Olver, Link to a section of the Digital Library of Mathematical Functions.

FORMULA

G.f. A(x) satisfies 216x^2A(x)''+(432x-1)A(x)'+30A(x)=0.

PROGRAM

(PARI) a(n)=if(n<0, 0, (6*n)!/(3*n)!/(2*n)!/2^n)

CROSSREFS

Sequence in context: A166834 A159401 A050984 this_sequence A059049 A056071 A137749

Adjacent sequences: A087213 A087214 A087215 this_sequence A087217 A087218 A087219

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 26 2003

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Last modified December 15 00:47 EST 2009. Contains 170825 sequences.


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