

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.


3



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
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OFFSET

0,3


LINKS



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[i1], 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()(nm*k, m1, concat(u, Vec(p)))*2^cross(p, u)*permcount(p)); s/k!))}


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



