A007145 Number of rooted bridgeless graphs with n nodes. (Formerly M3605)

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

Offset

1,4

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.

Prog

(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

Crossrefs

Cf. A004115, A007146.

Sequence in context: A182798 A073840 A024249 * A241000 A305988 A219530

Adjacent sequences: A007142 A007143 A007144 * A007146 A007147 A007148

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

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

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

Status

approved