A007145 Number of rooted bridgeless graphs with n nodes.

1, 0, 1, 4, 24, 193, 2420, 47912, 1600524, 93253226, 9694177479, 1822463625183, 625829508087155, 395785845695978077, 464137111800208818956, 1015091598240432264958267, 4160447480034069826186309689, 32088552194861245127627790541334

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..40 (terms 1..22 from R. J. Mathar, terms 21..22 corrected by Andrew Howroyd)
• P. Hanlon and R. W. Robinson, Counting bridgeless graphs, J. Combin. Theory, B 33 (1982), 276-305.

Crossrefs

Cf. A004115, A007146.

Programs

PARI

\\ See A004115 for graphsSeries and A339645 for combinatorial species functions.
cycleIndexSeries(n)={my(g=graphsSeries(n), gcr=sPoint(g)/g); sSolve( gcr, x*sv(1)*sExp(gcr) )}
NumUnlabeledObjsSeq(cycleIndexSeries(15)) \\ Andrew Howroyd, Dec 27 2020

Extensions

Reference gives first 22 terms (terms a(21) and a(22) contain typos).

More terms from R. J. Mathar, Jun 06 2007