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 A322395 Number of labeled 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. 23
 1, 1, 1, 4, 26, 548, 22504, 1708336, 241874928, 65285161232, 34305887955616, 35573982726480064, 73308270568902715136, 301210456065963448091072, 2471487759846321319412778624, 40526856087731237340916330352896, 1328570640536613080046570271722309632 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..50 Eric Weisstein's World of Mathematics, Graph Bridge Eric Weisstein's World of Mathematics, Endpoint FORMULA a(n) = n + Sum_{k=1..n} binomial(n,k)*A095983(k)*k^(n-k) for n >= 3. - Andrew Howroyd, Dec 07 2018 MATHEMATICA nmax = 16; seq[n_] := Module[{v, p, q, c}, v[_] = 0; p = x*D[#, x]& @ Log[Sum[ 2^Binomial[k, 2]*x^k/k!, {k, 0, n}] + O[x]^(n + 1)]; q = x*E^p; p -= q; For[k = 3, k <= n, k++, c = Coefficient[p, x, k]; v[k] = c*(k - 1)!; p -= c*q^k]; Join[{0}, Array[v, n]]]; A095983 = seq[nmax]; a[n_] := If[n<3, 1, n+Sum[Binomial[n, k]*A095983[[k+1]]*k^(n-k), {k, 1, n}]]; a /@ Range[0, nmax] (* Jean-François Alcover, Jan 07 2021, after Andrew Howroyd *) CROSSREFS Cf. A001187, A006125, A007146, A013922, A054921, A095983, A322338, A322387, A322394. Sequence in context: A328419 A194926 A167147 * A326264 A132488 A320626 Adjacent sequences:  A322392 A322393 A322394 * A322396 A322397 A322398 KEYWORD nonn AUTHOR Gus Wiseman, Dec 06 2018 EXTENSIONS a(6)-a(16) from Andrew Howroyd, Dec 07 2018 STATUS approved

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Last modified April 18 15:08 EDT 2021. Contains 343089 sequences. (Running on oeis4.)