The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A182932

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A182932

Generalized Bell numbers, row 3 of A182933.
(history; published version)

#7 by Bruno Berselli at Mon Jul 29 10:31:12 EDT 2013

STATUS

proposed

approved

#6 by Jean-François Alcover at Mon Jul 29 09:32:14 EDT 2013

STATUS

editing

proposed

#5 by Jean-François Alcover at Mon Jul 29 09:32:08 EDT 2013

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 *)

STATUS

approved

editing

#4 by T. D. Noe at Wed Mar 30 13:51:00 EDT 2011

STATUS

reviewed

approved

#3 by Olivier Gérard at Wed Mar 30 02:43:38 EDT 2011

STATUS

proposed

reviewed

#2 by Peter Luschny at Tue Mar 29 20:05:02 EDT 2011

NAME

allocated for Peter LuschnyGeneralized Bell numbers, row 3 of A182933.

DATA

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

OFFSET

0,2

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);

CROSSREFS

Cf. A182933, A000110, A094577.

KEYWORD

allocated

nonn

AUTHOR

Peter Luschny, Mar 29 2011

STATUS

approved

proposed

#1 by Peter Luschny at Mon Dec 13 20:53:31 EST 2010

NAME

allocated for Peter Luschny

KEYWORD

allocated

STATUS

approved