A244304 Number of standard Young tableaux with n cells such that the lengths of the first and the last row differ by 10.

11, 66, 923, 6761, 59631, 430135, 3286934, 22973870, 166443706, 1140859011, 8005160811, 54582972124, 377341672273, 2571480311931, 17687177703846, 120864485062762, 832211596826779, 5716894541334650, 39541329587796481, 273544962791156596, 1904469339140619197

Offset

12,1

Comments

Also the number of ballot sequences of length n such that the multiplicities of the largest and the smallest value differ by 10.

Links

Alois P. Heinz, Table of n, a(n) for n = 12..80

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=10, `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=12..35);

Crossrefs

Column k=10 of A238707.

Sequence in context: A030115 A091929 A345036 * A058883 A141969 A142645

Adjacent sequences: A244301 A244302 A244303 * A244305 A244306 A244307

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 25 2014

Status

approved