A005330 Certain subgraphs of a directed graph.

1, 5, 40, 644, 21496, 1471460, 204062440, 56865072164, 31688930152696, 35223651007587140, 78001790003385408040, 343983307379873262633284, 3020895063527811952260491896, 52843677532033943174017588842020, 1841795434229559227318546660111716840

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.

Programs

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) * 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) * 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