%I #17 Jan 01 2021 14:18:39

%S 1,1,1,2,5,18,98,779,10589,255790,11633297,1004417286,163944008107,

%T 50324877640599,29001521193534445,31396727025729968365,

%U 63969154112074956299242,245871360738448777028919520,1787330701747389106609369225312,24636017249593067184544456944967278

%N Number of unlabeled simple connected graphs with n vertices whose bridges are all leaves, meaning at least one end of any bridge is an endpoint of the graph.

%H Andrew Howroyd, <a href="/A322396/b322396.txt">Table of n, a(n) for n = 0..25</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphBridge.html">Graph Bridge</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Endpoint.html">Endpoint</a>

%H Gus Wiseman, <a href="/A322396/a322396.png">The a(5) = 18 simple connected graphs whose bridges are all leaves.</a>

%o (PARI) \\ See A004115 for graphsSeries and A339645 for combinatorial species functions.

%o bridgelessGraphs(n)={my(gc=sLog(graphsSeries(n)), gcr=sPoint(gc)); sSolve( gc + gcr^2/2 - sRaise(gcr,2)/2, x*sv(1)*sExp(gcr) )}

%o cycleIndexSeries(n)={1+sSubstOp(bridgelessGraphs(n), symGroupSeries(n))}

%o NumUnlabeledObjsSeq(cycleIndexSeries(15)) \\ _Andrew Howroyd_, Dec 31 2020

%Y Cf. A001187, A006125, A007146, A013922, A054921, A095983, A322338, A322394, A322395.

%K nonn

%O 0,4

%A _Gus Wiseman_, Dec 06 2018

%E a(6)-a(10) from _Andrew Howroyd_, Dec 08 2018

%E Terms a(11) and beyond from _Andrew Howroyd_, Dec 31 2020