A182932 Generalized Bell numbers, row 3 of A182933.
1, 13, 778, 104149, 25053583, 9566642254, 5355754528213, 4158610032552331, 4298349730542075004, 5729540573235706713253, 9603970716624058765049701, 19831898899231255981742972188, 49594487447520772034033468182501
Offset: 0
Keywords
Programs
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Maple
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: seq(A182932(n),n=0..12);
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Mathematica
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 *)
Formula
Let r = [4,...,4] (n occurrences of 4), s = [1,...,1,2] (n-1 occurrences of 1)
and F_n the generalized hypergeometric function of type n_F_n, then
a(n) = exp(-1)*3!^n*F_n(r,s |1).
e.g.f.: Sum_{j>=0}(exp((j+2)!/(j-1)!*x-1)/j!).