A340029 Number of unlabeled 2-connected graphs with n vertices rooted at a pair of indistinguishable vertices.

0, 1, 1, 6, 37, 388, 6004, 148759, 5974184, 404509191, 47552739892, 9923861406343, 3735194287263442, 2565376853616300801, 3244070698095148283628, 7607050619214875184974489, 33269229977451262849539412860, 272689940536978851416633440863567

Offset: 1

Author

Andrew Howroyd, Jan 02 2021

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..30

Crossrefs

Cf. A002218, A004115, A241768, A303829, A303831, A340028.

Programs

PARI

\\ See A004115 for graphsSeries and A339645 for combinatorial species functions.
blockGraphs(n)={my(gc=sLog(graphsSeries(n)), gcr=sPoint(gc)); intformal(x*sSolve( sLog( gcr/(x*sv(1)) ), gcr ), sv(1)) + sSolve(subst(gc, sv(1), 0), gcr)}
cycleIndexSeries(n)={sCartProd(blockGraphs(n), x^2 * symGroupCycleIndex(2) * symGroupSeries(n-2))}
{ my(N=15); Vec(OgfSeries(cycleIndexSeries(N)), -N) }