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

0,3

Links

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

Prog

(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!))))}

Crossrefs

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

Sequence in context: A264760 A090959 A244035 * A126942 A126947 A188494

Adjacent sequences: A340022 A340023 A340024 * A340026 A340027 A340028

Keyword

nonn

Author

Andrew Howroyd, Jan 01 2021

Status

approved