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%I #9 May 12 2016 15:20:35
%S 1,2,27,778,37553,2688546,265141267,34260962282,5594505151713,
%T 1123144155626338,271300013006911211,77489174023697484522,
%U 25797166716252173322577,9890278784047791697198658,4322087630240844404678150883
%N Generalized Bell numbers, column 2 of A182933.
%F a(n) = exp(-1)*n!^2*F_2([n+1,n+1],[1,2] |1), F_2 the generalized hypergeometric function of type 2_F_2.
%F Let b_{n}(x) = Sum_{j>=0}(x*exp((j+n-1)!/(j-1)!-1)/j!) then a(n) = 2 [x^2] series b_{n}(x), where [x^2] denotes the coefficient of x^2 in the Taylor series for b_{n}(x).
%p A182934 := proc(n)
%p exp(-x)*n!^2*hypergeom([n+1,n+1],[1,2],x); round(evalf(subs(x=1,%),66)) end:
%p seq(A182934(n),n=0..14);
%t a[n_] := n!^2*HypergeometricPFQ[{n+1, n+1}, {1, 2}, 1.`40.]/E; Table[a[n] // Round, {n, 0, 14}] (* _Jean-François Alcover_, Jul 29 2013 *)
%Y Cf. A182933, A000262.
%K nonn
%O 0,2
%A _Peter Luschny_, Mar 29 2011
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