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A244303 Number of standard Young tableaux with n cells such that the lengths of the first and the last row differ by 9. 2
10, 55, 714, 4796, 39544, 265589, 1899137, 12448912, 84901024, 547968340, 3633493460, 23423908430, 153474667719, 991845819899, 6480618983179, 42093506667304, 275840531014103, 1804204772698796, 11893232452570720, 78437868094585319, 521001980260102004 (list; graph; refs; listen; history; text; internal format)
OFFSET

11,1

COMMENTS

Also the number of ballot sequences of length n such that the multiplicities of the largest and the smallest value differ by 9.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 11..90

MAPLE

h:= proc(l) local n; n:=nops(l); add(i, i=l)!/mul(mul(1+l[i]-j+

    add(`if`(l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n) end:

g:= proc(n, i, l) local j; `if`(n=0 or i<1, 0, `if`(l<>[] and

      l[1]-i=9, `if`(irem(n, i, 'j')=0, h([l[], i$j]), 0),

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

    end:

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

seq(a(n), n=11..35);

CROSSREFS

Column k=9 of A238707.

Sequence in context: A001557 A197357 A164951 * A261848 A000814 A202071

Adjacent sequences:  A244300 A244301 A244302 * A244304 A244305 A244306

KEYWORD

nonn

AUTHOR

Joerg Arndt and Alois P. Heinz, Jun 25 2014

STATUS

approved

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Last modified October 2 23:51 EDT 2022. Contains 357230 sequences. (Running on oeis4.)