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A055152
Proper covers of an unlabeled n-set.
4
0, 1, 14, 956, 9331320, 6406603065901952, 16879085743296493569230716352778240, 717956902513121252476003434439730211883694285987816199468264943161704448
OFFSET
1,3
LINKS
Heller, Jürgen Identifiability in probabilistic knowledge structures. J. Math. Psychol. 77, 46-57 (2017).
Eric Weisstein's World of Mathematics, Proper covers
FORMULA
a(n) = (A003180(n) - 2*A003180(n-1))/4.
Apparently a(n) = A002857(n) - A000612(n-1). - R. J. Mathar, Apr 22 2007
MAPLE
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:
seq(a(n), n=1..8); # Alois P. Heinz, Aug 14 2019
MATHEMATICA
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;
a /@ Range[8] (* Jean-François Alcover, Feb 19 2020, after Alois P. Heinz in A000612 *)
CROSSREFS
See A007537 for labeled case. Cf. A055621.
Sequence in context: A350566 A199651 A241110 * A171183 A064729 A189304
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Jun 14 2000
EXTENSIONS
More terms from David Wasserman, Mar 21 2002
STATUS
approved