A111637 Number of labeled graphs having n blue nodes and n green ones, where edges join only nodes of different colors.

1, 4, 96, 10240, 4587520, 8455716864, 63496796504064, 1932044240141942784, 237409596228641929297920, 117555946699326540948428554240, 234206054295766751302924897412448256, 1875359927045089548108556844295368069873664

Offset: 0

Author

Emeric Deutsch, Aug 09 2005

Keywords

• nonn

Examples

			a(1) = 4 because we have B G, B--G, G B and G--B, where B (G) stands for a blue (green) node and -- denotes an edge.
		

References

• H. S. Wilf, Generatingfunctionology, 2nd edn., Academic Press, NY, 1994, p. 88.

Crossrefs

Cf. A111636, A000984, A002416.

Programs

Maple

a:= n-> 2^(n^2)*binomial(2*n,n): seq(a(n),n=0..12);

Formula

a(n) = C(2n,n) * 2^(n^2).

a(n) = A000984(n) * A002416(n).

a(n) = A111636(2n,n).