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A145455
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Exponential transform of C(n,5) = A000389.
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4
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1, 0, 0, 0, 0, 1, 6, 21, 56, 126, 378, 3234, 34056, 289575, 2020018, 12237225, 70634928, 468041756, 4190274648, 45557515620, 499503011496, 5121432107757, 49183015347774, 462331794763069, 4579813478536296, 50959878972009546
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OFFSET
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0,7
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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 5 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 5 labels.
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LINKS
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FORMULA
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E.g.f.: exp(exp(x)*x^5/5!).
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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, 5) *a(n-j), j=1..n))
end:
seq(a(n), n=0..30);
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MATHEMATICA
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With[{nmax = 50}, CoefficientList[Series[Exp[Exp[x]*x^5/5!], {x, 0, nmax}], x]] (* G. C. Greubel, Nov 21 2017 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(exp(exp(x)*x^5/5!))) \\ G. C. Greubel, Nov 21 2017
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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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