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%I #14 Dec 19 2021 12:08:08
%S 1,1,6,52,1540,145984,48467296,56141454464,229148555640864,
%T 3333310786076963968,174695272746896566439424,
%U 33301710992539090379269318144,23278728241293494584257987458067456,60084295633556503802059558812644803074048,576025077880237078776946976495257043823396069376
%N Number of unlabeled digraphs with loops (relations) on n nodes and with an even number of arcs.
%C Also relations considered equivalent when isomorphic and when complemented. - _Christian G. Bower_, Jan 05 2004
%H Andrew Howroyd, <a href="/A055973/b055973.txt">Table of n, a(n) for n = 0..50</a>
%F a(2*n) = (A000595(2*n) + A047832(n))/2; a(2*n+1) = A000595(2*n+1)/2.
%F a(n) = (A000595(n) + A000171(2*n+1))/2.
%F a(n) = sum {1*s_1+2*s_2+...=n, 1*t_1+2*t_2=2} (fixA[s_1, s_2, ...;t_1, t_2]/(1^s_1*s_1!*2^s_2*s_2!*...*1^t_1*t_1!*2^t_2*t_2!)) where fixA[...] = prod {i, j>=1} ( (sum {d|lcm(i, j)} (d*t_d))^(gcd(i, j)*s_i*s_j)) - _Christian G. Bower_, Jan 05 2004
%Y Cf. A000171, A000595, A007869, A047832, A054928, A055974.
%K easy,nonn
%O 0,3
%A _Vladeta Jovovic_, Jul 19 2000
%E a(0)=1 prepended and terms a(13) and beyond from _Andrew Howroyd_, Apr 19 2020
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