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A065950 Bessel polynomial {y_n}'''(1).

%I A065950 #17 Sep 23 2023 21:37:43
%S A065950 0,0,0,90,3150,81900,1992060,48771450,1237774230,32978969100,
%T A065950 927339227100,27566149731120,866148362679600,28735959507074820,
%U A065950 1005105838958594100,36999204981675832350,1430792213377354462530,58019598569681129648700
%N A065950 Bessel polynomial {y_n}'''(1).
%D A065950 J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.
%H A065950 G. C. Greubel, <a href="/A065950/b065950.txt">Table of n, a(n) for n = 0..400</a>
%H A065950 <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>
%F A065950 a(n) = 6*binomial(n, 3)*(1/2)_{n}*2^n*hypergeometric1f1(3-n, -2*n, 2), where (a)_{n} is the Pochhammer symbol. - _G. C. Greubel_, Aug 15 2017
%F A065950 G.f.: (90*x^3/(1-x)^7)*hypergeometric2f0(4,7/2; - ; 2*x/(1-x)^2). - _G. C. Greubel_, Aug 16 2017
%F A065950 a(n) ~ 2^(n + 1/2) * n^(n+3) / exp(n-1). - _Vaclav Kotesovec_, Jun 09 2019
%t A065950 Join[{0,0,0}, Table[6*Binomial[n,3]*Pochhammer[1/2,n]*2^n* Hypergeometric1F1[3-n,-2*n,2], {n,3,50}]] (* _G. C. Greubel_, Aug 15 2017 *)
%t A065950 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 A065950 (PARI) for(n=0,50, print1(sum(k=0,n-3, ((n+k+3)!/(2^(k+3)*k!*(n-k-3)!))), ", ")) \\ _G. C. Greubel_, Aug 15 2017
%o A065950 (Magma) [0,0,0] cat [(&+[Binomial(n-3,k)*Factorial(n+k+3)/(2^(k+3) * Factorial(n-3)): k in [0..n-3]]): n in [3..30]]; // _G. C. Greubel_, Sep 23 2023
%o A065950 (SageMath)
%o A065950 def A065950(n): return sum(binomial(n-3,k)*rising_factorial(n-2,k+6)//2^(k+3) for k in range(n-2))
%o A065950 [A065950(n) for n in range(31)] # _G. C. Greubel_, Sep 23 2023
%Y A065950 Cf. A001516, A001518.
%K A065950 nonn
%O A065950 0,4
%A A065950 _N. J. A. Sloane_, Dec 08 2001