A244302 Number of standard Young tableaux with n cells such that the lengths of the first and the last row differ by 8.

9, 45, 539, 3290, 25234, 156743, 1042823, 6374389, 40710734, 245996972, 1533537330, 9295148728, 57412881670, 349869872571, 2159393201713, 13252915145611, 82161769477646, 508497521855467, 3174435344149894, 19827435510586970, 124802677329672826

Offset

10,1

Comments

Also the number of ballot sequences of length n such that the multiplicities of the largest and the smallest value differ by 8.

Links

Alois P. Heinz, Table of n, a(n) for n = 10..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=8, `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=10..35);

Crossrefs

Column k=8 of A238707.

Sequence in context: A009432 A145757 A058824 * A177742 A322892 A355175

Adjacent sequences: A244299 A244300 A244301 * A244303 A244304 A244305

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 25 2014

Status

approved