A337716 Number of graphs, where vertices are labeled with positive integers summing to n, and where identically labeled vertices are indistinguishable and cannot be connected with an edge.

1, 1, 2, 4, 8, 16, 35, 77, 179, 440, 1160, 3264, 9950, 33206, 121943, 494011, 2235399, 11391306, 65287199, 422908306, 3130775625, 26490210964, 255257056748, 2825013955541, 36147331371446, 531237157370531, 8965348473026888

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..50 (terms 0..30 from Max Alekseyev)

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}
cross(u, v) = {sum(i=1, #u, sum(j=1, #v, gcd(u[i], v[j])))}
R(n, m, u)={if(n==0, 1, sum(k=if(m==1, n, 0), n\m, my(s=0); forpart(p=k, s+=self()(n-m*k, m-1, concat(u, Vec(p)))*2^cross(p, u)*permcount(p)); s/k!))}
a(n)={R(n, n, [])} \\ Andrew Howroyd, Sep 18 2020

Crossrefs

Cf. A337717.

Sequence in context: A034339 A244519 A247293 * A126137 A085294 A195327

Adjacent sequences: A337713 A337714 A337715 * A337717 A337718 A337719

Keyword

nonn

Author

Max Alekseyev following a suggestion from Franklin T. Adams-Watters, Sep 16 2020

Status

approved