A244303 Number of standard Young tableaux with n cells such that the lengths of the first and the last row differ by 9.

10, 55, 714, 4796, 39544, 265589, 1899137, 12448912, 84901024, 547968340, 3633493460, 23423908430, 153474667719, 991845819899, 6480618983179, 42093506667304, 275840531014103, 1804204772698796, 11893232452570720, 78437868094585319, 521001980260102004

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: A367938 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