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A145458
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Exponential transform of C(n,8) = A000581.
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3
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1, 0, 0, 0, 0, 0, 0, 0, 1, 9, 45, 165, 495, 1287, 3003, 6435, 19305, 243100, 3981978, 49959702, 498967170, 4190469570, 30728937690, 201931408074, 1213163827326, 6849350570700, 39615797628550, 296414654550300, 3418235092302030
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OFFSET
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0,10
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COMMENTS
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a(n) is the number of ways of placing n labeled balls into indistinguishable boxes, where in each filled box 8 balls are seen at the top.
a(n) is also the number of forests of labeled rooted trees of height at most 1, with n labels, where each root contains 8 labels.
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LINKS
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FORMULA
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E.g.f.: exp(exp(x)*x^8/8!).
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1,
add(binomial(n-1, j-1) *binomial(j, 8) *a(n-j), j=1..n))
end:
seq(a(n), n=0..35);
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MATHEMATICA
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With[{nn=30}, CoefficientList[Series[Exp[Exp[x] x^8/8!], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Feb 05 2020 *)
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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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