%I #12 Aug 17 2017 05:54:06

%S 0,0,6,-150,3870,-110670,3538500,-125941284,4953759300,-213744815460,

%T 10047637214010,-511403305348650,28029852267603186,

%U -1646397200571955650,103190849406195456360,-6875135229835376875560,485256294032090950981800

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

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

%H G. C. Greubel, <a href="/A065946/b065946.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), where (a)_{n} is the Pochhammer symbol.

%F E.g.f.: (1/16)*(1 + 4*x)^(-5/2)*((24*x^2 + 20*x + 2)*sqrt(1 + 4*x) + (16*x^3 - 12*x^2 - 24*x - 2))*exp((sqrt(1 + 4*x) -1)/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)*

%t 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)!))*(-1)^k), ", ")) \\ _G. C. Greubel_, Aug 14 2017

%Y Cf. A001518, A001516.

%K sign

%O 0,3

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