A179521 The number of (nontrivial) cycles in the symmetric group S_2n that involve equally many elements in {1,...,n} and {n+1,...,2n}.

0, 1, 10, 183, 7192, 501505, 54163866, 8349297775, 1738661539168, 469966765754097, 159953336512367770, 66922241946410591191, 33756538093718717040600, 20201172267759560773858513, 14150039840975130413592164362, 11468217024458648756976754157295

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

a(n) = Sum_{k=1..n} (2k-1)! binomial(n,k)^2.

Maple

a:= n-> add((2*k-1)!*binomial(n, k)^2, k=1..n):
seq(a(n), n=0..20);  # Alois P. Heinz, Jun 14 2015

Prog

(PARI) a(n) = sum(k=1, n, (2*k-1)! * binomial(n, k)^2); \\ Michel Marcus, Aug 14 2013

Crossrefs

Sequence in context: A304936 A239764 A364987 * A211102 A121973 A223146

Adjacent sequences: A179518 A179519 A179520 * A179522 A179523 A179524

Keyword

nonn

Author

Lukas Brantner (dlbb2(AT)cam.ac.uk), Jul 17 2010

Extensions

More terms from Michel Marcus, Aug 14 2013

Status

approved