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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A293128 Number of standard Young tableaux of 2n cells and height <= n. 3
1, 1, 6, 51, 588, 7990, 126060, 2242618, 44546320, 977152266, 23500234512, 615372604033, 17442275104496, 532242021137346, 17399782340548920, 606732491690590816, 22477989291826848000, 881635273413199806994, 36493478646922003374096, 1589642562747880936613248 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also the number of standard Young tableaux of 2n cells and <= n columns.

Also the number of 2n-length words w over n-ary alphabet {a1,a2,...,an} such that for every prefix z of w we have #(z,a1) >= #(z,a2) >= ... >= #(z,an), where #(z,x) counts the letters x in word z. The a(2) = 6 words of length 4 over alphabet {a,b} are: aaaa, aaab, aaba, abaa, aabb, abab.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..41 (terms 0..32 from Alois P. Heinz)

Wikipedia, Young tableau

FORMULA

a(n) = A182172(2n,n).

MAPLE

h:= l-> (n-> add(i, i=l)!/mul(mul(1+l[i]-j+add(`if`(l[k]

     <j, 0, 1), k=i+1..n), j=1..l[i]), i=1..n))(nops(l)):

g:= (n, i, l)-> `if`(n=0 or i=1, h([l[], 1$n]), add(

               g(n-i*j, i-1, [l[], i$j]), j=0..n/i)):

a:= n-> g(2*n, n, []):

seq(a(n), n=0..15);

CROSSREFS

Cf. A182172, A267436.

Sequence in context: A113352 A063169 A246189 * A304185 A215003 A134525

Adjacent sequences:  A293125 A293126 A293127 * A293129 A293130 A293131

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 30 2017

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 20 13:59 EDT 2018. Contains 316379 sequences. (Running on oeis4.)