%I #13 Aug 17 2017 05:50:34
%S 0,0,6,-240,9540,-415590,20134590,-1082674404,64221641820,
%T -4173853100670,295282282905720,-22605059036265420,
%U 1862664627479732076,-164425432052147568120,15483794266369962976170,-1549617160894627918342620,164264715996348003982855020
%N Bessel polynomial {y_n}''(-3).
%D J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.
%H G. C. Greubel, <a href="/A065948/b065948.txt">Table of n, a(n) for n = 0..340</a>
%H <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>
%F From _G. C. Greubel_, Aug 15 2017: (Start)
%F a(n) = 4*n*(n - 1)*(1/2)_{n}*(-6)^(n - 2)* hypergeometric1f1(2 - n; -2*n; -2/3), where (a)_{n} is the Pochhammer symbol.
%F E.g.f.: (-1/81)*(1 + 6*x)^(-5/2)*((-99*x^2 - 54*x - 4)*sqrt(1 + 6*x) + (-54*x^3 + 66*x + 4))*exp(-(1 - sqrt(1 + 6*x))/3). (End)
%F G.f.: (6*x^2/(1-x)^5)*hypergeometric2f0(3,5/2; - ; -6*x/(1-x)^2). - _G. C. Greubel_, Aug 16 2017
%t Join[{0, 0}, Table[4*n*(n - 1)*Pochhammer[1/2, n]*(-6)^(n - 2)* Hypergeometric1F1[2 - n, -2*n, -2/3], {n, 2, 50}]] (* _G. C. Greubel_, Aug 15 2017 *)
%o (PARI) for(n=0,50, print1(sum(k=0,n-2, ((n+k+2)!/(4*k!*(n-k-2)!))*(-3/2)^k ), ", ")) \\ _G. C. Greubel_, Aug 15 2017
%Y Cf. A001518, A001516.
%K sign
%O 0,3
%A _N. J. A. Sloane_, Dec 08 2001