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A262320
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Number of ways to select a subset s from an n-set and then partition s into blocks of equal size.
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4
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1, 2, 5, 12, 30, 73, 191, 528, 1553, 5032, 18088, 66905, 266382, 1164517, 5215645, 23868104, 117740144, 609872351, 3268548407, 18110463456, 102867877415, 620476915966, 4005216028162, 25747549921339, 166978155172421, 1168774024335204, 8556355097320142
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OFFSET
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0,2
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LINKS
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FORMULA
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E.g.f.: exp(x) * (1 + Sum_{k>=1} (exp(x^k/k!)-1)).
a(n) = 1 + Sum_{k=1..n} C(n,k) * A038041(k).
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EXAMPLE
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a(3) = 12: {}, 1, 2, 3, 12, 1|2, 13, 1|3, 23, 2|3, 123, 1|2|3.
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MAPLE
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b:= proc(n) option remember;
add(1/(d!*(n/d)!^d), d=numtheory[divisors](n))
end:
a:= n-> 1 + n! * add(b(k)/(n-k)!, k=1..n):
seq(a(n), n=0..30);
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MATHEMATICA
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b[n_] := b[n] = DivisorSum[n, 1/(#!*(n/#)!^#)&]; a[n_] := 1 + n! * Sum[b[k]/(n-k)!, {k, 1, n}]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Dec 18 2016, after Alois P. Heinz *)
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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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