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Number of graphs with loops on 2n unlabeled vertices with n loops.
2

%I #8 Mar 11 2023 19:46:27

%S 1,2,28,1408,580656,2658827456,146702084635392,98485306566812364032,

%T 820443196111261227164076544,86804253216450161933010414314819072,

%U 119212631345634236227720012129209606659383296,2166023316743980619769969171366251471253351621687457792

%N Number of graphs with loops on 2n unlabeled vertices with n loops.

%C a(n) is the number of bicolored graphs on 2n unlabeled nodes with an equal number of each color. Adjacent vertices may have the same color.

%H Andrew Howroyd, <a href="/A361405/b361405.txt">Table of n, a(n) for n = 0..25</a>

%F a(n) = A361404(2*n, n).

%o (PARI) a(n) = row(2*n)[n+1] \\ row(n) defined in A361404.

%Y Central coefficients of A361404.

%Y Cf. A007139.

%K nonn

%O 0,2

%A _Andrew Howroyd_, Mar 11 2023