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A006199 Bessel polynomial {y_n}'(-1).

%I A006199 M3082 #32 Aug 18 2017 09:40:03
%S A006199 0,1,-3,21,-185,2010,-25914,386407,-6539679,123823305,-2593076255,
%T A006199 59505341676,-1484818160748,40025880386401,-1159156815431055,
%U A006199 35891098374564105,-1183172853341759129,41372997479943753582,-1529550505546305534414,59608871544962952539335
%N A006199 Bessel polynomial {y_n}'(-1).
%C A006199 Absolute values give partitions into pairs.
%D A006199 G. Kreweras and Y. Poupard, Sur les partitions en paires d'un ensemble fini totalement ordonné, Publications de l'Institut de Statistique de l'Université de Paris, 23 (1978), 57-74.
%D A006199 J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.
%D A006199 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006199 G. C. Greubel, <a href="/A006199/b006199.txt">Table of n, a(n) for n = 1..400</a>
%H A006199 <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>
%F A006199 a(n) = A000806(n) + (n-1) * A000806(n-1). - _Sean A. Irvine_, Jan 23 2017
%F A006199 From _G. C. Greubel_, Aug 14 2017: (Start)
%F A006199 a(n) = 2*n*(1/2)_{n} * (-2)^(n-1) * hyergeometric1f1(1-n; -2*n; -2), where (a)_{n} is the Pochhammer symbol.
%F A006199 E.g.f.: (1+2*x)^(-3/2)*( (1+2*x)^(3/2) - x*(1+2*x)^(1/2) - x -1) * exp(sqrt(1+2*x) - 1), for offset 0. (End)
%F A006199 G.f.: (x/(1-x)^3)*hypergeometric2f0(2,3/2; - ; -2*x/(1-x)^2), for offset 0. - _G. C. Greubel_, Aug 16 2017
%t A006199 Join[{0}, Table[2*n*Pochhammer[1/2, n]*(-2)^(n - 1)* Hypergeometric1F1[1 - n, -2*n, -2], {n,1,50}]] (* _G. C. Greubel_, Aug 14 2017 *)
%o A006199 (PARI) for(n=0,50, print1(sum(k=0,n-1, ((n+k)!/(k!*(n-k)!))*(-1/2)^k), ", ")) \\ _G. C. Greubel_, Aug 14 2017
%Y A006199 Cf. A000806, A001514, A065707, A065920, A065921, A065922.
%K A006199 sign
%O A006199 1,3
%A A006199 _N. J. A. Sloane_