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 A055621 Number of covers of an unlabeled n-set. 60
 1, 1, 4, 34, 1952, 18664632, 12813206150470528, 33758171486592987151274638874693632, 1435913805026242504952006868879460423801146743462225386100617731367239680 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 78 (2.3.39) LINKS Alois P. Heinz, Table of n, a(n) for n = 0..12 Eric Weisstein's World of Mathematics, Cover FORMULA a(n) = (A003180(n) - A003180(n-1))/2 = A000612(n) - A000612(n-1) for n>0. Euler transform of A323819. - Gus Wiseman, Aug 14 2019 EXAMPLE There are 4 nonisomorphic covers of {1,2}, namely {{1},{2}}, {{1,2}}, {{1},{1,2}} and {{1},{2},{1,2}}. From Gus Wiseman, Aug 14 2019: (Start) Non-isomorphic representatives of the a(3) = 34 covers:   {123}  {1}{23}    {1}{2}{3}      {1}{2}{3}{23}          {13}{23}   {1}{3}{23}     {1}{2}{13}{23}          {3}{123}   {2}{13}{23}    {1}{2}{3}{123}          {23}{123}  {2}{3}{123}    {2}{3}{13}{23}                     {3}{13}{23}    {1}{3}{23}{123}                     {12}{13}{23}   {2}{3}{23}{123}                     {1}{23}{123}   {3}{12}{13}{23}                     {3}{23}{123}   {2}{13}{23}{123}                     {13}{23}{123}  {3}{13}{23}{123}                                    {12}{13}{23}{123} .   {1}{2}{3}{13}{23}     {1}{2}{3}{12}{13}{23}    {1}{2}{3}{12}{13}{23}{123}   {1}{2}{3}{23}{123}    {1}{2}{3}{13}{23}{123}   {2}{3}{12}{13}{23}    {2}{3}{12}{13}{23}{123}   {1}{2}{13}{23}{123}   {2}{3}{13}{23}{123}   {3}{12}{13}{23}{123} (End) 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-> `if`(n=0, 2, b(n\$2, [])-b(n-1\$2, []))/2: seq(a(n), n=0..8);  # Alois P. Heinz, Aug 14 2019 MATHEMATICA b[n_, i_, l_] := b[n, i, l] = If[n==0, 2^Function[w, Sum[Product[2^GCD[t, l[[h]]], {h, 1, Length[l]}], {t, 1, w}]/w][If[l=={}, 1, LCM@@l]], If[i<1, 0, Sum[b[n-i*j, i-1, Join[l, Table[i, {j}]]]/j!/i^j, {j, 0, n/i}]]]; a[n_] := If[n==0, 2, b[n, n, {}] - b[n-1, n-1, {}]]/2; a /@ Range[0, 8] (* Jean-François Alcover, Jan 31 2020, after Alois P. Heinz *) CROSSREFS Unlabeled set-systems are A000612 (partial sums). The version with empty edges allowed is A003181. The labeled version is A003465. The T_0 case is A319637. The connected case is A323819. The T_1 case is A326974. Cf. A058891, A319559, A326946, A326973. Sequence in context: A088077 A162079 A113231 * A000860 A222397 A193994 Adjacent sequences:  A055618 A055619 A055620 * A055622 A055623 A055624 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Jun 04 2000 EXTENSIONS More terms from David Moews (dmoews(AT)xraysgi.ims.uconn.edu) Jul 04 2002 a(0) = 1 prepended by Gus Wiseman, Aug 14 2019 STATUS approved

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Last modified February 22 15:26 EST 2020. Contains 332137 sequences. (Running on oeis4.)