%I A138364
%S A138364 0,1,0,3,0,10,0,35,0,126,0,462,0,1716,0,6435,0,24310,0,92378,0,352716,
               0,
%T A138364 1352078,0,5200300,0,20058300,0,77558760,0,300540195,0,1166803110,0,
%U A138364 4537567650,0,17672631900,0,68923264410,0,269128937220,0
%N A138364 Coefficients of I_1(2z) where I_1 is the hyperbolic Bessel function of 
               order 1.
%C A138364 An aerated version of A001700, which is the main entry for this sequence.
%D A138364 Kiran S. Kedlaya and Andrew V. Sutherland, "Hyperelliptic curves, L-polynomials 
               and random matrices", preprint, 2008.
%D A138364 Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Ch. 49, Hemisphere 
               Publishing Corp., 1999.
%H A138364 Kiran S. Kedlaya and Andrew V. Sutherland, <a href="http://arXiv.org/
               abs/0803.4462">Hyperelliptic curves, L-polynomials and random matrices</
               a>.
%F A138364 a(n)=binomial(n,(n+1)/2) for n odd, 0 otherwise. egf is I_1(2z).
%e A138364 a(5)=10 since the coefficient of z^5 in I_1(2z) is binomial(5,3)=10.
%Y A138364 Cf. A001700, A126869.
%Y A138364 Sequence in context: A167352 A094472 A028850 this_sequence A095364 A094052 
               A161678
%Y A138364 Adjacent sequences: A138361 A138362 A138363 this_sequence A138365 A138366 
               A138367
%K A138364 easy,nonn
%O A138364 0,4
%A A138364 Andrew V. Sutherland (drew(AT)math.mit.edu), Mar 16 2008