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

0, 1, 14, 170, 2904, 74779, 2751790, 137080628, 8882440224, 726325289493, 73173672616318, 8906815805139614, 1288823180820993752, 218690604655001166063, 43009037666992387906942, 9705063652363696926178792, 2490696756572714604529691648, 721374035463654709543727643561

Offset

1,3

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Formula

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).

Prog

(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}

Crossrefs

Column 2 of A286418.

Sequence in context: A200164 A199529 A098299 * A254811 A099158 A014882

Adjacent sequences: A341497 A341498 A341499 * A341501 A341502 A341503

Keyword

nonn

Author

Andrew Howroyd, Feb 21 2021

Status

approved