OFFSET
1,2
COMMENTS
Number of atomic permutations with three runs of equal length n.
LINKS
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
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 26 2014
STATUS
approved