login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
1, 11, 181, 3499, 73501, 1623467, 37081045, 867484331, 20661914989, 499049420011, 12188943245909, 300438089843371, 7461880085538581, 186524863637339819, 4688354828111460181, 118407620161890380459, 3002994055439841324301, 76441823131542496027499, 1952230701520399696996501, 50003999526279431605603499 (list; graph; refs; listen; history; text; internal format)
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: A020456 A036935 A205088 * A143413 A009118 A321848

Adjacent sequences:  A241190 A241191 A241192 * A241194 A241195 A241196

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 26 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 13:50 EST 2019. Contains 329877 sequences. (Running on oeis4.)