A361404 Triangle read by rows: T(n,k) is the number of graphs with loops on n unlabeled vertices with k loops.
1, 1, 1, 2, 2, 2, 4, 6, 6, 4, 11, 20, 28, 20, 11, 34, 90, 148, 148, 90, 34, 156, 544, 1144, 1408, 1144, 544, 156, 1044, 5096, 13128, 20364, 20364, 13128, 5096, 1044, 12346, 79264, 250240, 472128, 580656, 472128, 250240, 79264, 12346
Offset: 0
Examples
Triangle begins:
1;
1, 1;
2, 2, 2;
4, 6, 6, 4;
11, 20, 28, 20, 11;
34, 90, 148, 148, 90, 34;
156, 544, 1144, 1408, 1144, 544, 156;
1044, 5096, 13128, 20364, 20364, 13128, 5096, 1044;
...
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)
Crossrefs
Programs
-
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) = {sum(i=2, #v, sum(j=1, i-1, gcd(v[i], v[j]))) + sum(i=1, #v, v[i]\2)} row(n) = {my(s=0); forpart(p=n, s+=permcount(p)*2^edges(p)*prod(i=1, #p, 1 + x^p[i])); Vecrev(s/n!)}
Formula
T(n,k) = T(n, n-k).
Comments