A126067 Triangle read by rows: T(n,k) is the number of unlabeled self-converse digraphs with n nodes and k arcs, k=0..n*(n-1).

1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 3, 5, 9, 10, 12, 10, 9, 5, 3, 1, 1, 1, 1, 3, 6, 15, 24, 41, 57, 77, 84, 90, 84, 77, 57, 41, 24, 15, 6, 3, 1, 1, 1, 1, 3, 7, 20, 42, 91, 164, 295, 463, 683, 918, 1185, 1394, 1550, 1590, 1550, 1394, 1185, 918, 683, 463, 295, 164, 91, 42, 20, 7, 3, 1, 1

Offset

0,8

Links

Andrew Howroyd, Table of n, a(n) for n = 0..2680 (rows 0..20)

Example

Triangle begins:
  1;
  1;
  1,1,1;
  1,1,2,2,2,1,1;
  1,1,3,5,9,10,12,10,9,5,3,1,1;
  1,1,3,6,15,24,41,57,77,84,90,84,77,57,41,24,15,6,3,1,1;
  ....

Prog

(PARI)
permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}
edges(v, t) = {prod(i=2, #v, prod(j=1, i-1, my(c=gcd(v[i], v[j])*if(v[i]*v[j]%2==0, 2, 1)); t(2*v[i]*v[j]/c)^c)) * prod(i=1, #v, my(c=v[i]); if(c%2, t(2*c)^(c\2), t(c)^(c-1-c%4/2)*t(c/2)^(c%4)))}
Row(n) = {my(s=0); forpart(p=n, s+=permcount(p)*edges(p, i->1+x^i)); Vecrev(s)/n!}
{ for(n=0, 5, print(Row(n))) } \\ Andrew Howroyd, Apr 19 2020

Crossrefs

Row sums are A002499.

Cf. A052283, A126066.

Sequence in context: A346118 A309797 A199840 * A327490 A346529 A238408

Adjacent sequences: A126064 A126065 A126066 * A126068 A126069 A126070

Keyword

nonn,tabf

Author

Vladeta Jovovic, Feb 28 2007

Extensions

a(0)=1 prepended and terms a(46) and beyond from Andrew Howroyd, Apr 19 2020

Status

approved