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

0,2

References

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

Links

Table of n, a(n) for n=0..11.

Formula

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

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

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

Example

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.

Maple

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

Crossrefs

Cf. A111636, A000984, A002416.

Sequence in context: A190196 A065140 A007106 * A027872 A308146 A203517

Adjacent sequences: A111634 A111635 A111636 * A111638 A111639 A111640

Keyword

nonn

Author

Emeric Deutsch, Aug 09 2005

Status

approved