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 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 5 05:37 EST 2023. Contains 367575 sequences. (Running on oeis4.)