cp's OEIS Frontend

A378324 Number of cyclic edge cuts in the complete graph K_n.

%I A378324 #17 May 27 2025 14:59:18
%S A378324 0,0,0,0,0,10,840,57428,4323760,428530774,66698370662,19304350714396,
%T A378324 11435576322977378,13998454986272457974,34730539006860778387488,
%U A378324 172307954877667746584363616,1699711619922134215461075979752,33269167602899548362529088074829390
%N A378324 Number of cyclic edge cuts in the complete graph K_n.
%H A378324 Eric W. Weisstein, <a href="/A378324/b378324.txt">Table of n, a(n) for n = 1..100</a>
%H A378324 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CompleteGraph.html">Complete Graph</a>.
%H A378324 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CyclicEdgeCut.html">Cyclic Edge Cut</a>.
%F A378324 E.g.f.: (exp(B(x)-T(x))-(B(x)-T(x))-1)*exp(T(x)-1) where B(x) is the e.g.f. of A001187 and T(x) is the e.g.f. of A000272. - _Andrew Howroyd_, Nov 26 2024
%F A378324 a(n) = A006125(n) - A001858(n) - Sum_{k=1..n} binomial(n,k)*(A001187(k)-A000272(k))*A001858(n-k). - _Andrew Howroyd_, May 27 2025
%t A378324 With[{n = 20},
%t A378324  B[x_] := 1 + Log[Sum[2^Binomial[k, 2] x^k/k!, {k, 0, n}]];
%t A378324  T[x_] := 1 - LambertW[-x] - LambertW[-x]^2/2;
%t A378324  Rest@CoefficientList[Series[(Exp[B[x] - T[x]] - (B[x] - T[x]) - 1) Exp[T[x] - 1], {x, 0, n}], x] Range[n]!
%t A378324 ]
%o A378324 (PARI) seq(n)={my(t=sum(k=1, n, k^(k-2)*x^k/k!, O(x*x^n)), c=log(sum(k=0, n, 2^binomial(k,2)*x^k/k!, O(x*x^n)))-t); Vec(serlaplace((exp(c)-1-c)*exp(t)), -n)} \\ _Andrew Howroyd_, Nov 26 2024
%Y A378324 Cf. A000272, A001187, A006125, A001858.
%K A378324 nonn
%O A378324 1,6
%A A378324 _Eric W. Weisstein_, Nov 23 2024
%E A378324 a(8) onwards from _Andrew Howroyd_, Nov 26 2024