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A145453
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Exponential transform of binomial(n,3) = A000292(n-2).
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8
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1, 0, 0, 1, 4, 10, 30, 175, 1176, 7084, 42120, 286605, 2270180, 19213766, 166326524, 1497096055, 14374680880, 147259920760, 1582837679056, 17659771122969, 204674606377140, 2473357218561250, 31148510170120420, 407154732691440811, 5504706823227724904
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OFFSET
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0,5
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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 3 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 3 labels.
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LINKS
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FORMULA
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E.g.f.: exp(exp(x)*x^3/3!).
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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, 3) *a(n-j), j=1..n))
end:
seq(a(n), n=0..30);
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MATHEMATICA
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Table[Sum[BellY[n, k, Binomial[Range[n], 3]], {k, 0, n}], {n, 0, 25}] (* Vladimir Reshetnikov, Nov 09 2016 *)
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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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