The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A323816 Number of set-systems covering n vertices with no singletons. 7
 1, 0, 1, 12, 1993, 67098768, 144115187673233113, 1329227995784915871895000745158568460, 226156424291633194186662080095093570015284114833799899660370362545578585265 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS G. C. Greubel, Table of n, a(n) for n = 0..11 FORMULA Inverse binomial transform of A016031 shifted once to the left. EXAMPLE The a(3) = 12 set-systems: {{1,2,3}} {{1,2}, {1,3}} {{1,2}, {2,3}} {{1,3}, {2,3}} {{1,2}, {1,2,3}} {{1,3}, {1,2,3}} {{2,3}, {1,2,3}} {{1,2}, {1,3}, {2,3}} {{1,2}, {1,3}, {1,2,3}} {{1,2}, {2,3}, {1,2,3}} {{1,3}, {2,3}, {1,2,3}} {{1,2}, {1,3}, {2,3}, {1,2,3}} MAPLE a:= n-> add(2^(2^(n-j)-n+j-1)*binomial(n, j)*(-1)^j, j=0..n): seq(a(n), n=0..8); # Alois P. Heinz, Jan 30 2019 MATHEMATICA Table[Sum[(-1)^(n-k)*Binomial[n, k]*2^(2^k-k-1), {k, 0, n}], {n, 0, 8}] PROG (Magma) [(&+[(-1)^(n-j)*Binomial(n, j)*2^(2^j -j-1): j in [0..n]]): n in [0..12]]; // G. C. Greubel, Oct 05 2022 (SageMath) def A323816(n): return sum((-1)^j*binomial(n, j)*2^(2^(n-j) -n+j-1) for j in range(n+1)) [A323816(n) for n in range(12)] # G. C. Greubel, Oct 05 2022 CROSSREFS Cf. A000295, A000371, A000612, A003465 (with singletons), A006129 (covers by pairs), A016031, A055154, A055621, A305001, A317795 (unlabeled case), A323817 (connected case). Sequence in context: A011920 A323817 A263584 * A208252 A204622 A369336 Adjacent sequences: A323813 A323814 A323815 * A323817 A323818 A323819 KEYWORD nonn AUTHOR Gus Wiseman, Jan 30 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 23 06:04 EDT 2024. Contains 371906 sequences. (Running on oeis4.)