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A144223
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Number of ways of placing n labeled balls into n unlabeled (but 6-colored) boxes.
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15
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1, 6, 42, 330, 2850, 26682, 268098, 2869242, 32510850, 388109562, 4861622850, 63682081530, 869725707522, 12352785293562, 182049635623362, 2778394592545530, 43833623157604482, 713738052924821754
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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FORMULA
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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
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MAPLE
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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:
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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