A040996 -id:A040996 - cp's OEIS frontend

A318129 Number of sets of nonempty subsets of {1,...,n} with intersection {}.

1, 1, 3, 91, 31827, 2147158387, 9223372011085950171, 170141183460469231602560095290109272523, 57896044618658097711785492504343953923912733397452774312538303978325772978595

Offset: 0

Gus Wiseman, Aug 18 2018

nonn

			The a(2) = 3 sets of sets are {}, {{1},{2}}, {{1},{2},{1,2}}.

Cf. A000371, A001146, A003465,A040996, A119563, A131288.

Cf. A318128, A318130, A318131, A318132.

Table[Length[Select[Subsets[Rest[Subsets[Range[n]]]],Or[#=={},Intersection@@#=={}]&]],{n,0,4}]

Binomial transform of A318128.

a(n) = A318130(n) - 2^(2^n - 1). [corrected]

A111403 a(n) = f(f(n+1)) - f(f(n)), where f(m) = 2^m.

Original entry on oeis.org

2, 12, 240, 65280, 4294901760, 18446744069414584320, 340282366920938463444927863358058659840, 115792089237316195423570985008687907852929702298719625575994209400481361428480

Offset: 0

N. J. A. Sloane, Nov 12 2005

nonn

			The binary representation of the first values shows what is going on:
10
1100
11110000
1111111100000000
11111111111111110000000000000000
...

Alois P. Heinz, Table of n, a(n) for n = 0..10

Probably equal to A087046(n+2). Doubled A040996.

a:= n-> (p-> p*(p-1))(2^(2^n)):
seq(a(n), n=0..7);  # Alois P. Heinz, Jan 03 2018

Conjecture: a(n) = A002716(2*n)-1. - R. J. Mathar, May 15 2007
From Alois P. Heinz, Jan 03 2018: (Start)
a(n) = 2^(2*2^n) - 2^(2^n).
a(n) = p*(p-1) with p = 2^(2^n). (End)
a(n) = A040996(n) * 2. - Tilman Piesk, Oct 04 2024

Example and cross-reference from Olivier Gérard, Jun 23 2014

cp's OEIS Frontend

A318129 Number of sets of nonempty subsets of {1,...,n} with intersection {}.

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