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 A065920 #18 Aug 17 2017 03:08:29
%S A065920 0,1,15,246,4810,111315,2994621,92069740,3188772756,122934101445,
%T A065920 5223324100555,242563221769506,12224586738476190,664572113979550231,
%U A065920 38767776344788218105,2415639337342677314520,160131212043826343202856
%N A065920 Bessel polynomial {y_n}'(2).
%D A065920 J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.
%H A065920 G. C. Greubel, <a href="/A065920/b065920.txt">Table of n, a(n) for n = 0..360</a>
%H A065920 <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>
%F A065920 Recurrence: (n-1)^2*a(n) = (2*n - 1)*(2*n^2 - 2*n + 1)*a(n-1) + n^2*a(n-2). - _Vaclav Kotesovec_, Jul 22 2015
%F A065920 a(n) ~ 2^(2*n-1/2) * n^(n+1) / exp(n-1/2). - _Vaclav Kotesovec_, Jul 22 2015
%F A065920 From _G. C. Greubel_, Aug 14 2017: (Start)
%F A065920 a(n) = 2*n*(1/2)_{n}*4^(n - 1)* hypergeometric1f1(1 - n, -2*n, 1).
%F A065920 E.g.f.: ((1 - 4*x)^(3/2) + 2*x*(1 - 4*x)^(1/2) + 8*x - 1)*exp((1 - sqrt(1 - 4*x))/2)/(4*(1 - 4*x)^(3/2)). (End)
%F A065920 G.f.: (t/(1-t)^3)*hypergeometric2f0(2,3/2; - ; 4*t/(1-t)^2). - _G. C. Greubel_, Aug 16 2017
%t A065920 Table[Sum[(n+k+1)!/(2*(n-k-1)!*k!), {k,0,n-1}], {n,0,20}] (* _Vaclav Kotesovec_, Jul 22 2015 *)
%t A065920 Join[{0}, Table[2*n*Pochhammer[1/2, n]*4^(n - 1)* Hypergeometric1F1[1 - n, -2*n, 1], {n,1,50}]] (* _G. C. Greubel_, Aug 14 2017 *)
%o A065920 (PARI) for(n=0,50, print1(sum(k=0,n-1, (n+k+1)!/(2*(n-k-1)!*k!)), ", ")) \\ _G. C. Greubel_, Aug 14 2017
%Y A065920 Cf. A001514, A065921, A065922.
%K A065920 nonn
%O A065920 0,3
%A A065920 _N. J. A. Sloane_, Dec 08 2001