%I M2992 N1212 #25 Oct 19 2015 01:27:30
%S 0,0,0,0,1,3,15,79,474,3207,24087,198923,1791902,17484377,183707380,
%T 2067904033,24827519376,316694549817,4277112686513,60971132411393,
%U 914869422343564,14413525170009350,237888443951757586,4104608160094692304
%N Coefficients in the asymptotic expansions of modified Hankel functions h_1(z) and h_2(z), rounded to nearest integer.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D 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.
%H Robert Israel, <a href="/A002514/b002514.txt">Table of n, a(n) for n = 1..459</a>
%H The Staff of the Computational Laboratory, <a href="/A002514/a002514.pdf">Tables of the Modified Hankel Functions of Order One-Third and of Their Derivatives.</a> [Annotated scans of two pages]
%F 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
%F a(n) = round(Gamma(n+5/6)*Gamma(n+1/6)*3^n/(2^(2*n+1)*Pi*n!)). - _Robert Israel_, Oct 19 2015
%p 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
%K nonn
%O 1,6
%A _N. J. A. Sloane_
%E More terms from _Sean A. Irvine_, Oct 18 2015