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%I #15 Dec 25 2017 04:02:47
%S 1,2,45,3045,434700,109596375,43800340815,25797179878470,
%T 21243510135522675,23503974546075598575,33865310276598741840900,
%U 61964234361152712204340725,141027420945032510510113517025
%N Bell(2n)*(2n-1)!!, where Bell are the Bell numbers A000110.
%C This sequence arises in the normal ordering problem the exponential of square of boson number operator.
%F a(n) = Bell(2*n)*(2*n)!/(2^n*n!) = A001147(n)*A000110(2*n).
%F E.g.f.: G(x) = Sum_{k>=0} exp((k*x)^2/2-1)/k!; a(n) = subs(x=0, (d^(2n)/dx^(2n))G(x)).
%t Array[BellB[2 #] (2 # - 1)!! &, 13, 0] (* _Michael De Vlieger_, Dec 24 2017 *)
%o (PARI) a(n)=round(exp(-1)*suminf(k=0,k^(2*n)/k!))*(2*n)!/(2^n*n!) \\ _Charles R Greathouse IV_, Nov 06 2011
%Y Cf. A000110, A001147.
%K nonn
%O 0,2
%A _Karol A. Penson_, Nov 03 2004