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

1,4

Links

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

Prog

(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) }

Crossrefs

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

Sequence in context: A288703 A337552 A036358 * A185036 A185236 A041062

Adjacent sequences: A340026 A340027 A340028 * A340030 A340031 A340032

Keyword

nonn

Author

Andrew Howroyd, Jan 02 2021

Status

approved