A340025 Number of connected graphs with vertices labeled with positive integers summing to n.

1, 1, 2, 4, 12, 41, 210, 1478, 17128, 352926, 14181309, 1129005180, 175491164826, 52346463432414, 29666505555854777, 31806668884174645842, 64442744342933382243031, 246898165053174167804654086, 1791518193851453375966274280997, 24668222649527263942329934357240780

Offset: 0

Author

Andrew Howroyd, Jan 01 2021

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A001349, A337717, A340022, A340026, A340027.

Programs

PARI

\\ See A340022 for permcount, edges.
InvEulerT(v)={my(p=log(1+x*Ser(v))); dirdiv(vector(#v,n,polcoef(p,n)), vector(#v,n,1/n))}
seq(n) = {concat([1], InvEulerT(Vec(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!))))}