A221159 a(n) = Sum_{i=0..n} Stirling2(n,i)*2^(3i).

1, 8, 72, 712, 7624, 87496, 1067976, 13781448, 187104200, 2661876168, 39549629384, 611918940616, 9834596715464, 163824830616008, 2823080829871048, 50238768569014728, 921839901090823112, 17416746966515278280, 338394913332895863752, 6753431112631087835592, 138296031340416209103816

Offset: 0

Author

N. J. A. Sloane, Jan 04 2013

Keywords

• nonn

Comments

The number of ways of putting n labeled balls into a set of bags and then putting the bags into 8 labeled boxes. - Peter Bala, Mar 23 2013

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Frank Simon, Algebraic Methods for Computing the Reliability of Networks, Dissertation, Doctor Rerum Naturalium (Dr. rer. nat.), Fakultät Mathematik und Naturwissenschaften der Technischen Universität Dresden, 2012. See Table 5.1.

Crossrefs

Cf. A000110, A001861, A078944, A221176, A027710, A144180, A144223, A144263, A189233.

Programs

Mathematica

Table[BellB[n,8],{n,0,20}] (* Vaclav Kotesovec, Mar 12 2014 *)

Formula

E.g.f.: exp(8*(exp(x) - 1)). - Peter Bala, Mar 23 2013

a(n) ~ n^n * exp(n/LambertW(n/8)-8-n) / (sqrt(1+LambertW(n/8)) * LambertW(n/8)^n). - Vaclav Kotesovec, Mar 12 2014

G.f.: Sum_{j>=0} 8^j*x^j / Product_{k=1..j} (1 - k*x). - Ilya Gutkovskiy, Apr 11 2019