OFFSET
0,8
COMMENTS
Also the number of unlabeled loop-graphs covering n vertices with k loops and n-k non-loops such that each connected component has the same number of edges as vertices.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)
EXAMPLE
Triangle begins:
1
0 1
0 1 1
1 2 1 1
2 5 3 1 1
5 12 7 3 1 1
14 29 19 8 3 1 1
35 75 47 21 8 3 1 1
MATHEMATICA
Table[Length[Union[sysnorm /@ Select[Subsets[Subsets[Range[n], {1, 2}], {n}], Count[#, {_}]==k && Length[Select[Tuples[#], UnsameQ@@#&]]!=0&]]], {n, 0, 5}, {k, 0, n}]
PROG
TreeGf(N)={my(A=vector(N, j, 1)); for (n=1, N-1, A[n+1] = 1/n * sum(k=1, n, sumdiv(k, d, d*A[d]) * A[n-k+1] ) ); x*Ser(A)}
G(n, y)={my(t=TreeGf(n)); my(g(e)=subst(t + O(x*x^(n\e)), x, x^e) + O(x*x^n)); 1 + (sum(d=1, n, eulerphi(d)/d*log(1/(1-g(d)))) + ((1+g(1))^2/(1-g(2))-1)/2 - (g(1)^2 + g(2)))/2 + (y-1)*g(1)}
EulerMTS(p)={my(n=serprec(p, x)-1, vars=variables(p)); exp(sum(i=1, n, substvec(p + O(x*x^(n\i)), vars, apply(v->v^i, vars))/i))}
T(n)={[Vecrev(p) | p <- Vec(EulerMTS(G(n, y) - 1))]}
{ my(A=T(8)); for(n=1, #A, print(A[n])) } \\ Andrew Howroyd, Jan 14 2024
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Jan 13 2024
EXTENSIONS
a(36) onwards from Andrew Howroyd, Jan 14 2024
STATUS
approved