A005332 Certain subgraphs of a directed graph.

1, 7, 58, 838, 25171, 1610977, 214838128, 58540023808, 32208188445841, 35543124039418147, 78391002506394742198, 344921660620756227029578, 3025372940760065880037836511, 52886001393832278158415800800117, 1842588406743140390123203185385824268, 127974225758895121562137768141145597226148

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• E. Andresen, K. Kjeldsen, On certain subgraphs of a complete transitively directed graph, Discrete Math. 14 (1976), no. 2, 103-119.

Crossrefs

Cf. A005330.

Programs

Mathematica

p[n_]:=Product[2^k-1, {k,n}]; a[n_]:=Sum[(Binomial[n-1, i] * p[n-1-i] * 2^i*Sum [(-1)^j*(n-1-i-j)/p[j], {j,0,n-2-i}] ), {i,0,n-2}]; Table[a[n], {n,2,17}] (* Stefano Spezia, Sep 07 2022 *)

PARI

p(n) = prod(k=1, n, 2^k-1);
a(n) = sum(i=0, n-2, binomial(n-1, i) * p(n-1-i) * 2^i * sum(j=0, n-2-i, (-1)^j * (n-1-i-j) / p(j))); \\ Michel Marcus, May 10 2016

Formula

a(n) = Sum_{i=0..n-2} (C(n-1, i) * p(n-1-i) * 2^i * Sum_{j=0..n-2-i} (-1)^j * (n-1-i-j) / p(j)) where p(n) = Product_{k=1..n} (2^k-1). - Sean A. Irvine, May 10 2016

Extensions

More terms from Sean A. Irvine, May 10 2016