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

%I #8 Jun 14 2015 16:49:58

%S 0,1,10,183,7192,501505,54163866,8349297775,1738661539168,

%T 469966765754097,159953336512367770,66922241946410591191,

%U 33756538093718717040600,20201172267759560773858513,14150039840975130413592164362,11468217024458648756976754157295

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

%H Alois P. Heinz, <a href="/A179521/b179521.txt">Table of n, a(n) for n = 0..200</a>

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

%p a:= n-> add((2*k-1)!*binomial(n,k)^2, k=1..n):

%p seq(a(n), n=0..20); # _Alois P. Heinz_, Jun 14 2015

%o (PARI) a(n) = sum(k=1, n, (2*k-1)! * binomial(n, k)^2); \\ _Michel Marcus_, Aug 14 2013

%K nonn

%O 0,3

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

%E More terms from _Michel Marcus_, Aug 14 2013

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Last modified May 23 22:02 EDT 2024. Contains 372765 sequences. (Running on oeis4.)