This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A065944 #21 Sep 08 2022 08:45:04
%S A065944 0,0,6,-60,720,-9870,153510,-2679264,51934680,-1107917910,25807660560,
%T A065944 -651977992380,17758547202396,-518856566089680,16188283372489410,
%U A065944 -537210169663283760,18894951642157260480,-702160022681408982114
%N A065944 Bessel polynomial {y_n}''(-1).
%D A065944 J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.
%H A065944 G. C. Greubel, <a href="/A065944/b065944.txt">Table of n, a(n) for n = 0..400</a>
%H A065944 <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>
%F A065944 Recurrence: (n-2)*(n-1)*a(n) = -(n-2)*(n+1)*(2*n-1)*a(n-1) + n*(n+1)*a(n-2). - _Vaclav Kotesovec_, Jul 22 2015
%F A065944 a(n) ~ (-1)^n * 2^(n+1/2) * n^(n+2) / exp(n+1). - _Vaclav Kotesovec_, Jul 22 2015
%F A065944 From _G. C. Greubel_, Aug 14 2017: (Start)
%F A065944 a(n) = 2*n*(n-1)*(1/2)_{n}*(-2)^(n - 1)* hypergeometric1f1(2 - n, -2*n, -2), where (a)_{n} is the Pochhammer symbol.
%F A065944 E.g.f.: (1 + 2*x)^(-5/2)*(x*(x + 2)*sqrt(1 + 2*x) + (2*x^3 - 2*x)) * exp(-1 + sqrt(1 + 2*x)). (End)
%F A065944 G.f.: (6*x^2/(1-x)^5)*hypergeometric2f0(3,5/2; - ; -2*x/(1-x)^2). - _G. C. Greubel_, Aug 16 2017
%t A065944 Table[Sum[(n+k+2)!*(-1)^k/(2^(k+2)*(n-k-2)!*k!), {k,0,n-2}], {n,0,20}] (* _Vaclav Kotesovec_, Jul 22 2015 *)
%t A065944 Join[{0, 0}, Table[4*n*(n-1)*Pochhammer[1/2, n]*(-2)^(n-2)* Hypergeometric1F1[2-n, -2*n, -2], {n, 2,20}]] (* _G. C. Greubel_, Aug 14 2017 *)
%o A065944 (PARI) for(n=0,20, print1(sum(k=0,n-2, (n+k+2)!*(-1)^k/(2^(k+2)*(n-k-2)!*k!)), ", ")) \\ _G. C. Greubel_, Aug 14 2017
%o A065944 (Magma) f:=Factorial; [0,0] cat [(&+[((-1)^k*f(n+k+2)/(2^(k+2)*f(n-k-2) *f(k))): k in [0..n-2]]): n in [2..20]]; // _G. C. Greubel_, Jul 10 2019
%o A065944 (Sage) f=factorial; [0,0]+[sum((-1)^k*f(n+k+2)/(2^(k+2)*f(n-k-2)*f(k)) for k in (0..n-2)) for n in (2..20)] # _G. C. Greubel_, Jul 10 2019
%o A065944 (GAP) f:=Factorial;; Concatenation([0,0], List([2..20], n-> Sum([0..n-2], k-> (-1)^k*f(n+k+2)/(2^(k+2)*f(n-k-2)*f(k)) ))); # _G. C. Greubel_, Jul 10 2019
%Y A065944 Cf. A001518, A001516.
%K A065944 sign
%O A065944 0,3
%A A065944 _N. J. A. Sloane_, Dec 08 2001