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 A055152 Proper covers of an unlabeled n-set. 3
 0, 1, 14, 956, 9331320, 6406603065901952, 16879085743296493569230716352778240, 717956902513121252476003434439730211883694285987816199468264943161704448 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..12 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 Adjacent sequences:  A055149 A055150 A055151 * A055153 A055154 A055155 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Jun 14 2000 EXTENSIONS More terms from David Wasserman, Mar 21 2002 STATUS approved

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Last modified January 24 08:03 EST 2022. Contains 350534 sequences. (Running on oeis4.)