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A221159
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a(n) = Sum_{i=0..n} Stirling2(n,i)*2^(3i).
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12
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1, 8, 72, 712, 7624, 87496, 1067976, 13781448, 187104200, 2661876168, 39549629384, 611918940616, 9834596715464, 163824830616008, 2823080829871048, 50238768569014728, 921839901090823112, 17416746966515278280, 338394913332895863752, 6753431112631087835592, 138296031340416209103816
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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 8 labeled boxes. - Peter Bala, Mar 23 2013
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LINKS
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FORMULA
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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
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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