cp's OEIS Frontend

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

%I A111637 #12 Apr 03 2023 09:29:41
%S A111637 1,4,96,10240,4587520,8455716864,63496796504064,1932044240141942784,
%T A111637 237409596228641929297920,117555946699326540948428554240,
%U A111637 234206054295766751302924897412448256,1875359927045089548108556844295368069873664
%N A111637 Number of labeled graphs having n blue nodes and n green ones, where edges join only nodes of different colors.
%D A111637 H. S. Wilf, Generatingfunctionology, 2nd edn., Academic Press, NY, 1994, p. 88.
%F A111637 a(n) = C(2n,n) * 2^(n^2).
%F A111637 a(n) = A000984(n) * A002416(n).
%F A111637 a(n) = A111636(2n,n).
%e A111637 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.
%p A111637 a:= n-> 2^(n^2)*binomial(2*n,n): seq(a(n),n=0..12);
%Y A111637 Cf. A111636, A000984, A002416.
%K A111637 nonn
%O A111637 0,2
%A A111637 _Emeric Deutsch_, Aug 09 2005