OFFSET
0,1
COMMENTS
Also the number of non-isomorphic sets of subsets of {1..n} with union {1..n}. - Gus Wiseman, Aug 05 2019
REFERENCES
S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 38 and 214.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..12
S. Muroga, Threshold Logic and Its Applications, Wiley, NY, 1971. [Annotated scans of a few pages]
FORMULA
a(n) = 2 * A055621(n). - Gus Wiseman, Aug 05 2019
EXAMPLE
From Gus Wiseman, Aug 05 2019: (Start)
Non-isomorphic representatives of the a(0) = 2 through a(2) = 8 sets of subsets:
{} {{1}} {{1,2}}
{{}} {{},{1}} {{1},{2}}
{{},{1,2}}
{{2},{1,2}}
{{},{1},{2}}
{{},{2},{1,2}}
{{1},{2},{1,2}}
{{},{1},{2},{1,2}}
(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, [])):
seq(a(n), n=0..8); # Alois P. Heinz, Aug 14 2019
MATHEMATICA
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, {}]];
a /@ Range[0, 8] (* Jean-François Alcover, Apr 11 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Christian Sievers, Jul 22 2016
Definition clarified by Ivo Timoteo, Mar 14 2017
STATUS
approved