A340022 Number of graphs with vertices labeled with positive integers summing to n.
1, 1, 3, 7, 22, 71, 319, 1939, 19790, 377259, 14603435, 1144417513, 176665721300, 52525450429119, 29719386740326525, 31836493683553082697, 64474640381705842520802, 246962703426353769596309789, 1791765285568042699367722904797, 24670014908867411635732865067513309
Offset: 0
Keywords
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..50
Programs
-
Mathematica
permcount[v_] := Module[{m = 1, s = 0, k = 0, t}, For[i = 1, i <= Length[v], i++, t = v[[i]]; k = If[i > 1 && t == v[[i - 1]], k + 1, 1]; m *= t*k; s += t]; s!/m]; edges[v_] := Sum[GCD[v[[i]], v[[j]]], {i, 2, Length[v]}, {j, 1, i - 1}] + Total[Quotient[v, 2]]; seq[n_] := 1 + Sum[s = 0; Do[s += permcount[p]*2^edges[p]*x^k/Product[1 - x^p[[j]] + O[x]^(n-k+1), {j, 1, Length[p]}],{p, IntegerPartitions[k]}]; s/k!, {k, 1, n}] // CoefficientList[#, x]&; seq[19] (* Jean-François Alcover, Jan 06 2021, after Andrew Howroyd *) -
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)} seq(n) = {Vec(1+sum(k=1, n, my(s=0); forpart(p=k, s+=permcount(p) * 2^edges(p) * x^k/prod(j=1, #p, 1 - x^p[j] + O(x^(n-k+1)))); s/k!))}