%I #12 Aug 17 2017 05:52:01

%S 0,0,6,210,6390,201810,6895140,257335596,10489055220,465303486780,

%T 22363517407770,1159112646836430,64499453473280826,

%U 3837361123234687230,243168894263042103720,16356164256377393353080,1164094991704907423494920

%N Bessel polynomial {y_n}''(2).

%D J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.

%H G. C. Greubel, <a href="/A065945/b065945.txt">Table of n, a(n) for n = 0..360</a>

%H <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>

%F From _G. C. Greubel_, Aug 14 2017: (Start)

%F a(n) = 4*n*(n - 1)*(1/2)_{n}*4^(n - 2)*hypergeometric1f1[(2-n, -2*n, 1).

%F E.g.f.: (-1/16)*(1 - 4*x)^(-5/2)*((56*x^2 - 44*x + 6)*sqrt(1 - 4*x) + (16*x^3 - 180*x^2 + 56*x - 6))*exp((1 - sqrt(1 - 4*x))/2). (End)

%F G.f.: (6*x^2/(1-x)^5)*hypergeometric2f0(3,5/2; - ; 4*x/(1-x)^2). - _G. C. Greubel_, Aug 16 2017

%t Join[{0, 0}, Table[4*n*(n - 1)*Pochhammer[1/2, n]*4^(n - 2)* Hypergeometric1F1[2 - n, -2*n, 1], {n,2,50}]] (* _G. C. Greubel_, Aug 14 2017 *)

%o (PARI) for(n=0,50, print1(sum(k=0,n-2, ((n+k+2)!/(4*k!*(n-k-2)!))), ", ")) \\ _G. C. Greubel_, Aug 14 2017

%Y Cf. A001518, A001516.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Dec 08 2001