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A145454
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Exponential transform of binomial(n,4) = A000332.
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7
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1, 0, 0, 0, 1, 5, 15, 35, 105, 756, 6510, 46530, 283470, 1667380, 11457446, 99776040, 969295145, 9298091180, 86154691680, 804769174536, 8052676029420, 88489327173660, 1038440150703340, 12501684521410700, 151866259113256611
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OFFSET
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0,6
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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 4 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 4 labels.
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LINKS
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FORMULA
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E.g.f.: exp(exp(x)*x^4/4!).
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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, 4) *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], 4]], {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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