cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A341500 Number of cycles in the 2 X n rook graph.

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%I A341500 #9 Feb 22 2021 01:37:46
%S A341500 0,1,14,170,2904,74779,2751790,137080628,8882440224,726325289493,
%T A341500 73173672616318,8906815805139614,1288823180820993752,
%U A341500 218690604655001166063,43009037666992387906942,9705063652363696926178792,2490696756572714604529691648,721374035463654709543727643561
%N A341500 Number of cycles in the 2 X n rook graph.
%H A341500 Andrew Howroyd, <a href="/A341500/b341500.txt">Table of n, a(n) for n = 1..200</a>
%F A341500 a(n) = (Sum_{k=3..n} binomial(n,k)*(k-1)!) + (1/2)*Sum_{k=1..floor(n/2)} (k*binomial(n,2*k) * binomial(2*k,k) * (Sum_{j=0..n-2*k} binomial(n-2*k,j)*(k+j-1)!)^2).
%o A341500 (PARI) a(n)={sum(k=3, n, binomial(n,k)*(k-1)!) + sum(k=1, n\2, k*binomial(n,2*k) * binomial(2*k,k) * sum(j=0, n-2*k, binomial(n-2*k,j)*(k+j-1)!)^2)/2}
%Y A341500 Column 2 of A286418.
%K A341500 nonn
%O A341500 1,3
%A A341500 _Andrew Howroyd_, Feb 21 2021