A182932 Generalized Bell numbers, row 3 of A182933.

1, 13, 778, 104149, 25053583, 9566642254, 5355754528213, 4158610032552331, 4298349730542075004, 5729540573235706713253, 9603970716624058765049701, 19831898899231255981742972188, 49594487447520772034033468182501

Offset

0,2

Links

Table of n, a(n) for n=0..12.

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!).

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);

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 *)

Crossrefs

Cf. A182933, A000110, A094577.

Sequence in context: A033509 A262099 A301644 * A221934 A328033 A366559

Adjacent sequences: A182929 A182930 A182931 * A182933 A182934 A182935

Keyword

nonn

Author

Peter Luschny, Mar 29 2011

Status

approved