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%I #11 Jan 29 2016 06:09:46
%S 1,1,2,3,6,12,28,69,182,497,1399,4028,11852,35626,109494,344338,
%T 1108565,3653536,12320940,42483305,149640000,537975261,1972713660,
%U 7374794356,28100132482,109117922021,431821675389,1741507272791
%N Generalized Bessel numbers.
%C Hankel transform of a(n) is 1,1,1,... (by construction). Hankel transform of a(n+1) is A145063.
%C Is this the same as the sequence s(n) that can be seen in Fig. 8 of Zhang (2015), with a different offset? - _N. J. A. Sloane_, Jan 28 2016
%H Yan X Zhang, <a href="http://arxiv.org/abs/1508.00318">Four Variations on Graded Posets</a>, arXiv preprint arXiv:1508.00318 [math.CO], 2015.
%F G.f.: 1/(1-x-x^2/(1-0x-x^2/(1-2x-x^2/(1-0x-x^2/(1-3x-x^2/...))))) (a continued fraction).
%F G.f.: 1/(U(0)+x^2) where U(k)= 1 - x*(k+1) - 2*x^2 - x^4/U(k+1) ; (continued fraction, 3rd kind, 3-step). - _Sergei N. Gladkovskii_, Oct 23 2012
%Y Cf. A006789.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Sep 30 2008
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