A241193 a(n) = Sum_{k=1..n} ((3*n-k-1)/(2*n-k))*(3*n-k-2)!/((n-1)!*(n-1)!*(n-k)!).

1, 11, 181, 3499, 73501, 1623467, 37081045, 867484331, 20661914989, 499049420011, 12188943245909, 300438089843371, 7461880085538581, 186524863637339819, 4688354828111460181, 118407620161890380459, 3002994055439841324301, 76441823131542496027499, 1952230701520399696996501, 50003999526279431605603499

Offset

1,2

Comments

Number of atomic permutations with three runs of equal length n.

Links

Table of n, a(n) for n=1..20.

C. J. Fewster, D. Siemssen, Enumerating Permutations by their Run Structure, arXiv preprint arXiv:1403.1723 [math.CO], 2014.

Formula

Conjecture: -(2*n-1)*(n-1)^2*a(n) +2*(32*n^3-131*n^2+187*n-94)*a(n-1) +3*(-86*n^3+721*n^2-1896*n+1617)*a(n-2) -18*(2*n-5)*(3*n-8)*(3*n-7)*a(n-3)=0. - R. J. Mathar, Aug 26 2014

Maple

A241193:=n->add( ((3*n-k-1)/(2*n-k))*(3*n-k-2)!/((n-1)!*(n-1)!*(n-k)!), k=1..n);
[seq(A241193(n), n=1..40)];

Mathematica

a[n_] := Sum[((3n-k-1)/(2n-k))(3n-k-2)!/((n-1)! (n-1)! (n-k)!), {k, 1, n}];
Array[a, 20] (* Jean-François Alcover, Oct 08 2018 *)

Prog

(PARI) a(n) = sum(k=1, n, ((3*n-k-1)/(2*n-k))*(3*n-k-2)!/((n-1)!*(n-1)!*(n-k)!));

Crossrefs

Sequence in context: A036935 A205088 A388046 * A143413 A009118 A321848

Adjacent sequences: A241190 A241191 A241192 * A241194 A241195 A241196

Keyword

nonn

Author

N. J. A. Sloane, Apr 26 2014

Status

approved