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A111637
Number of labeled graphs having n blue nodes and n green ones, where edges join only nodes of different colors.
1
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.
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
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Aug 09 2005
STATUS
approved