%I #16 Jul 25 2022 15:41:25
%S 0,0,0,90,-1890,36540,-729540,15507450,-353908170,8680615020,
%T -228436914420,6431738433120,-193144902350400,6166945337372820,
%U -208728050864680620,7467661073819689470,-281666767117960443870,11173071188540083124700
%N Bessel polynomial {y_n}'''(-1).
%D J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.
%H G. C. Greubel, <a href="/A065951/b065951.txt">Table of n, a(n) for n = 0..400</a>
%H <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>
%F a(n) = 48*binomial(n,3)*(1/2)_{n}*(-2)^(n - 3)*hypergeometric1f1(3-n, -2*n, -2), where (a)_{n} is the Pochhammer symbol. - _G. C. Greubel_, Aug 15 2017
%F G.f.: (90*x^3/(1-x)^7)*hypergeometric2f0(4,7/2; - ; -2*x/(1-x)^2). - _G. C. Greubel_, Aug 16 2017
%F D-finite with recurrence (-n+3)*a(n) +(-2*n^2+11)*a(n-1) +(-2*n^2+8*n+3)*a(n-2) +(n+1)*a(n-3)=0. - _R. J. Mathar_, Jul 25 2022
%t Join[{0, 0, 0}, Table[48*Binomial[n, 3]*Pochhammer[1/2, n]*(-2)^(n - 3)* Hypergeometric1F1[3 - n, -2*n, -2], {n,3,50}]] (* _G. C. Greubel_, Aug 15 2017 *)
%t CoefficientList[Series[(90*t^3/(1 - t)^7)*HypergeometricPFQ[{4, 7/2}, {}, -2*t/(1 - t)^2], {t, 0, 50}], t] (* _G. C. Greubel_, Aug 16 2017 *)
%o (PARI) for(n=0,50, print1(sum(k=0,n-3, ((n+k+3)!/(8*(n-k-3)!*k!))*(-2)^k ), ", ")) \\ _G. C. Greubel_, Aug 15 2017
%Y Cf. A001518, A001516.
%K sign
%O 0,4
%A _N. J. A. Sloane_, Dec 08 2001