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A145456
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Exponential transform of C(n,6) = A000579.
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3
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1, 0, 0, 0, 0, 0, 1, 7, 28, 84, 210, 462, 1386, 13728, 171171, 1686685, 13461448, 91495768, 551777772, 3142726692, 19787406360, 172188951144, 1999835600301, 24655331721867, 285725747201356, 3034790658153100, 29876851476502030
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OFFSET
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0,8
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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 6 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 6 labels.
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LINKS
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FORMULA
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E.g.f.: exp(exp(x)*x^6/6!).
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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, 6) *a(n-j), j=1..n))
end:
seq(a(n), n=0..30);
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MATHEMATICA
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With[{nn=30}, CoefficientList[Series[Exp[Exp[x] x^6/6!], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Apr 14 2018 *)
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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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