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A055152
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Proper covers of an unlabeled n-set.
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4
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OFFSET
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1,3
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LINKS
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FORMULA
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MAPLE
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b:= proc(n, i, l) `if`(n=0, 2^(w-> add(mul(2^igcd(t, l[h]),
h=1..nops(l)), t=1..w)/w)(ilcm(l[])), `if`(i<1, 0,
add(b(n-i*j, i-1, [l[], i$j])/j!/i^j, j=0..n/i)))
end:
a:= n-> (b(n$2, [])-2*b(n-1$2, []))/4:
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MATHEMATICA
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b[n_] := Sum[1/Function[p, Product[Function[c, j^c*c!][Coefficient[p, x, j]], {j, 1, Exponent[p, x]}]][Total[x^l]]*2^(Function[w, Sum[Product[ 2^GCD[t, l[[i]]], {i, 1, Length[l]}], {t, 1, w}]/w][If[l == {}, 1, LCM @@ l]]), {l, IntegerPartitions[n]}];
a[n_] := (b[n] - 2 b[n - 1])/4;
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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