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 A144223 Number of ways of placing n labeled balls into n unlabeled (but 6-colored) boxes. 15
 1, 6, 42, 330, 2850, 26682, 268098, 2869242, 32510850, 388109562, 4861622850, 63682081530, 869725707522, 12352785293562, 182049635623362, 2778394592545530, 43833623157604482, 713738052924821754 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) is also the exp transform of A010722. - Alois P. Heinz, Oct 09 2008 The number of ways of putting n labeled balls into a set of bags and then putting the bags into 6 labeled boxes. - Peter Bala, Mar 23 2013 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..200 N. J. A. Sloane, Transforms FORMULA a(n) = Sum_{k=0..n} 6^k*A048993(n,k); A048993: Stirling2 numbers. G.f.: 6*(x/(1-x))*A(x/(1-x)) = A(x)-1; six times the binomial transform equals this sequence shifted one place left. E.g.f.: exp(6(e^x-1)). G.f.: T(0)/(1-6*x), where T(k) = 1 - 6*x^2*(k+1)/(6*x^2*(k+1) - (1-6*x-x*k)*(1-7*x-x*k)/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Dec 04 2013 a(n) ~ n^n * exp(n/LambertW(n/6)-6-n) / (sqrt(1+LambertW(n/6)) * LambertW(n/6)^n). - Vaclav Kotesovec, Mar 12 2014 G.f.: Sum_{j>=0} 6^j*x^j / Product_{k=1..j} (1 - k*x). - Ilya Gutkovskiy, Apr 07 2019 MAPLE a:= proc(n) option remember; `if`(n=0, 1,       (1+add(binomial(n-1, k-1)*a(n-k), k=1..n-1))*6)     end: seq(a(n), n=0..25); # Alois P. Heinz, Oct 09 2008 MATHEMATICA Table[BellB[n, 6], {n, 0, 20}] (* Vaclav Kotesovec, Mar 12 2014 *) PROG (Sage) expnums(18, 6) # Zerinvary Lajos, May 15 2009 CROSSREFS Cf. A000110, A001861, A027710, A078944, A144180. A144263, A189233, A221159, A221176. Sequence in context: A218755 A165314 A082302 * A320758 A262671 A029588 Adjacent sequences:  A144220 A144221 A144222 * A144224 A144225 A144226 KEYWORD nonn AUTHOR Philippe Deléham, Sep 14 2008 EXTENSIONS More terms from Alois P. Heinz, Oct 09 2008 STATUS approved

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Last modified June 23 01:56 EDT 2021. Contains 345394 sequences. (Running on oeis4.)