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 A221159 a(n) = Sum_{i=0..n} Stirling2(n,i)*2^(3i). 12
 1, 8, 72, 712, 7624, 87496, 1067976, 13781448, 187104200, 2661876168, 39549629384, 611918940616, 9834596715464, 163824830616008, 2823080829871048, 50238768569014728, 921839901090823112, 17416746966515278280, 338394913332895863752, 6753431112631087835592, 138296031340416209103816 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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. 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 MATHEMATICA Table[BellB[n, 8], {n, 0, 20}] (* Vaclav Kotesovec, Mar 12 2014 *) CROSSREFS Cf. A000110, A001861, A078944, A221176, A027710, A144180, A144223, A144263, A189233. Sequence in context: A220741 A165323 A082366 * A049388 A014479 A013992 Adjacent sequences:  A221156 A221157 A221158 * A221160 A221161 A221162 KEYWORD nonn AUTHOR N. J. A. Sloane, Jan 04 2013 STATUS approved

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Last modified January 18 09:26 EST 2022. Contains 350454 sequences. (Running on oeis4.)