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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A214955 Number of solid standard Young tableaux of shape [[n,n-1],[1]]. 2
1, 6, 25, 98, 378, 1452, 5577, 21450, 82654, 319124, 1234506, 4784276, 18572500, 72209880, 281150505, 1096087770, 4278278070, 16717354500, 65388738030, 256000696380, 1003116947820, 3933750236520, 15437682614250, 60625494924228, 238235373671148, 936735006679752 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is odd if and only if n = 2^i-1 for i in {1, 2, 3, ... } = A000027.

Form an array with m(1,n)=n*(n+1)/2, m(n,1)=n*(n-1)+1, and m(i,j)=m(i,j-1) + m(i-1,j); A000217 in the top row, A002061 in the first column, A086514 in the second column. Then on the diagonal m(n,n)=a(n). - J. M. Bergot, May 02 2013

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

S. B. Ekhad, D. Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux, arXiv:1202.6229v1 [math.CO], 2012

Wikipedia, Young tableau

FORMULA

a(n) = 2*(2*n-1)^2/((n+1)*(2*n-3)) * a(n-1) for n>1; a(1) = 1.

a(n) = (2*n-1) * C(2*n,n)/(n+1) = A060747(n) * A000108(n).

a(n) = [x^n] x*(1 + 2*x)/(1 - x)^(n+2). - Ilya Gutkovskiy, Oct 12 2017

MAPLE

a:= proc(n) option remember;

      `if`(n<2, n, 2*(2*n-1)^2*a(n-1)/((n+1)*(2*n-3)))

    end:

seq(a(n), n=1..30);

MATHEMATICA

a[n_]:= a[n] = If[n<2, n, 2*(2*n-1)^2*a[n-1]/((n+1)*(2*n-3))]; Array[a, 30] (* Jean-François Alcover, Aug 14 2017, translated from Maple *)

CROSSREFS

Column k=1 of A214775.

Cf. A000108, A060747, A215002.

Sequence in context: A034336 A291230 A092184 * A286433 A034559 A034347

Adjacent sequences:  A214952 A214953 A214954 * A214956 A214957 A214958

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 30 2012

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 March 25 12:11 EDT 2019. Contains 321470 sequences. (Running on oeis4.)