A244302 - OEIS

%I #5 Jun 26 2014 09:39:37

%S 9,45,539,3290,25234,156743,1042823,6374389,40710734,245996972,

%T 1533537330,9295148728,57412881670,349869872571,2159393201713,

%U 13252915145611,82161769477646,508497521855467,3174435344149894,19827435510586970,124802677329672826

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

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

%H Alois P. Heinz, <a href="/A244302/b244302.txt">Table of n, a(n) for n = 10..90</a>

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

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

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

%p       l[1]-i=8, `if`(irem(n, i, 'j')=0, h([l[], i$j]), 0),

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

%p     end:

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

%p seq(a(n), n=10..35);

%Y Column k=8 of A238707.

%K nonn

%O 10,1

%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 25 2014