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

0,3

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

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

Crossrefs

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

Sequence in context: A166889 A164894 A027835 * A223345 A362907 A369506

Adjacent sequences: A055970 A055971 A055972 * A055974 A055975 A055976

Keyword

easy,nonn

Author

Vladeta Jovovic, Jul 19 2000

Extensions

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

Status

approved