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%I #5 Jun 26 2014 13:02:10
%S 10,55,714,4796,39544,265589,1899137,12448912,84901024,547968340,
%T 3633493460,23423908430,153474667719,991845819899,6480618983179,
%U 42093506667304,275840531014103,1804204772698796,11893232452570720,78437868094585319,521001980260102004
%N Number of standard Young tableaux with n cells such that the lengths of the first and the last row differ by 9.
%C Also the number of ballot sequences of length n such that the multiplicities of the largest and the smallest value differ by 9.
%H Alois P. Heinz, <a href="/A244303/b244303.txt">Table of n, a(n) for n = 11..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=9, `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=11..35);
%Y Column k=9 of A238707.
%K nonn
%O 11,1
%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 25 2014
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