A055973 Number of unlabeled digraphs with loops (relations) on n nodes and with an even number of arcs.

1, 1, 6, 52, 1540, 145984, 48467296, 56141454464, 229148555640864, 3333310786076963968, 174695272746896566439424, 33301710992539090379269318144, 23278728241293494584257987458067456, 60084295633556503802059558812644803074048, 576025077880237078776946976495257043823396069376

Offset: 0

Author

Vladeta Jovovic, Jul 19 2000

Keywords

• easy
• nonn

Comments

Also relations considered equivalent when isomorphic and when complemented. - Christian G. Bower, Jan 05 2004

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A000171, A000595, A007869, A047832, A054928, A055974.

Formula

a(2*n) = (A000595(2*n) + A047832(n))/2; a(2*n+1) = A000595(2*n+1)/2.

a(n) = (A000595(n) + A000171(2*n+1))/2.

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

Extensions

a(0)=1 prepended and terms a(13) and beyond from Andrew Howroyd, Apr 19 2020