cp's OEIS Frontend

A377640 Number edge cuts in the n-cocktail party graph.

%I A377640 #13 Jun 12 2025 18:49:56
%S A377640 0,11,1440,2107526,42988931520,13507580252824616,
%T A377640 66106397544068778570240,5070456260407959009146349277616,
%U A377640 6125036729796414112360988978198319006720,116919909287476066493023898690514431465112835903616,35352620147125599712871920668133699973012391980925543664619520
%N A377640 Number edge cuts in the n-cocktail party graph.
%H A377640 Andrew Howroyd, <a href="/A377640/b377640.txt">Table of n, a(n) for n = 1..40</a>
%H A377640 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CocktailPartyGraph.html">Cocktail Party Graph</a>.
%H A377640 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EdgeCut.html">Edge Cut</a>.
%o A377640 (PARI)
%o A377640 B(m,n) = {16^binomial(m,2) * 2^binomial(n,2) * 4^(m*n)}
%o A377640 S(m,n)={ my(M=matrix(m+1,n+1,i,j,B(i-1,j-1)), N=matrix(m+1,n+1));
%o A377640   for(n=0, n, N[1,1+n] = M[1,1+n] - sum(j=1, n-1, binomial(n-1,j-1)*N[1,1+j]*M[1,1+n-j]));
%o A377640   for(m=1, m, for(n=0, n, N[1+m, 1+n] = M[1+m,1+n] - sum(i=1, m, sum(j=0, n, binomial(m-1,i-1)*binomial(n,j)*N[1+i,1+j]*M[1+m-i,1+n-j]))));
%o A377640   N
%o A377640 }
%o A377640 seq(n)=my(M=S(n,2*n)); vector(n, n, if(n==1, 0, 16^binomial(n,2) - sum(k=0, n, (-1)^k*binomial(n,k)*M[1+k, 1+2*(n-k)]))) \\ _Andrew Howroyd_, Jun 12 2025
%o A377640 (PARI)
%o A377640 D(n,i)={16^binomial(i,2)*sum(j=0, 2*(n-i), 2^binomial(j,2)*4^(i*j)*x^j/j!, O(x^(2*(n-i)+1)))}
%o A377640 E(n)={my(u=vector(n+1,i,D(n,i-1)), v=vector(n+1)); v[1]=1+log(u[1]); for(m=1, n, v[1+m] = (u[1+m] - sum(i=1, m-1, binomial(m-1,i-1)*v[1+i]*u[1+m-i]))/u[1] ); v}
%o A377640 seq(n)={my(u=E(n)); vector(n, n, if(n==1, 0, 16^binomial(n,2) - sum(k=0, n, (-1)^k*binomial(n,k)*(2*n-2*k)!*polcoef(u[1+k], 2*(n-k)) )))} \\ _Andrew Howroyd_, Jun 12 2025
%Y A377640 Cf. A297029.
%K A377640 nonn
%O A377640 1,2
%A A377640 _Eric W. Weisstein_, Nov 03 2024
%E A377640 a(5)-a(7) from _Andrew Howroyd_, May 27 2025
%E A377640 a(8) onwards from _Andrew Howroyd_, Jun 12 2025