A002514 Coefficients in the asymptotic expansions of modified Hankel functions h_1(z) and h_2(z), rounded to nearest integer. (Formerly M2992 N1212)

0, 0, 0, 0, 1, 3, 15, 79, 474, 3207, 24087, 198923, 1791902, 17484377, 183707380, 2067904033, 24827519376, 316694549817, 4277112686513, 60971132411393, 914869422343564, 14413525170009350, 237888443951757586, 4104608160094692304

Offset

1,6

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

The Staff of the Computational Laboratory, Tables of the Modified Hankel Functions of Order One-Third and of Their Derivatives. Annals of the Computation Laboratory of Harvard University, Vol. 2, Harvard Univ. Press, Cambridge, Massachusetts, 1945. see p. XXXV.

Links

Robert Israel, Table of n, a(n) for n = 1..459

The Staff of the Computational Laboratory, Tables of the Modified Hankel Functions of Order One-Third and of Their Derivatives. [Annotated scans of two pages]

Formula

a(n) = round((Product_{k=1..n} (9 * (2*k-1)^2 - 4)) / (2^(4*n) * 3^n * n!)). - Sean A. Irvine, Oct 18 2015

a(n) = round(Gamma(n+5/6)*Gamma(n+1/6)*3^n/(2^(2*n+1)*Pi*n!)). - Robert Israel, Oct 19 2015

Maple

seq(round(simplify(GAMMA(n+5/6)*GAMMA(n+1/6)*3^n/(2^(2*n+1)*Pi*n!))), n=1..50); # Robert Israel, Oct 19 2015

Crossrefs

Sequence in context: A292097 A052755 A137957 * A319216 A093889 A369085

Adjacent sequences: A002511 A002512 A002513 * A002515 A002516 A002517

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Oct 18 2015

Status

approved