%I #7 Jul 29 2013 10:31:12

%S 1,13,778,104149,25053583,9566642254,5355754528213,4158610032552331,

%T 4298349730542075004,5729540573235706713253,9603970716624058765049701,

%U 19831898899231255981742972188,49594487447520772034033468182501

%N Generalized Bell numbers, row 3 of A182933.

%F Let r = [4,...,4] (n occurrences of 4), s = [1,...,1,2] (n-1 occurrences of 1)

%F and F_n the generalized hypergeometric function of type n_F_n, then

%F a(n) = exp(-1)*3!^n*F_n(r,s |1).

%F e.g.f.: Sum_{j>=0}(exp((j+2)!/(j-1)!*x-1)/j!).

%p A182932 := proc(n) local r,s,i; r := [seq(4,i=1..n)]; s := [seq(1,i=1..n-1),2]; exp(-x)*6^n*hypergeom(r,s,x); round(evalf(subs(x=1,%),66)) end:

%p seq(A182932(n),n=0..12);

%t a[n_] := 3!^n*HypergeometricPFQ[ Table[4, {n}], Append[ Table[1, {n-1}], 2], 1.`40.]/E; Table[Round[a[n]], {n, 0, 12}] (* _Jean-François Alcover_, Jul 29 2013 *)

%Y Cf. A182933, A000110, A094577.

%K nonn

%O 0,2

%A Peter Luschny, Mar 29 2011