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A244300 Number of standard Young tableaux with n cells such that the lengths of the first and the last row differ by 6.

%I A244300 #5 Jun 25 2014 16:05:22
%S A244300 7,28,279,1354,8823,45553,256192,1328368,7272035,37498159,201732490,
%T A244300 1052038304,5628260010,29642509180,158744001098,844461334762,
%U A244300 4549886593291,24435491901926,132677029062176,719558882421952,3940213225673584,21584248413514700
%N A244300 Number of standard Young tableaux with n cells such that the lengths of the first and the last row differ by 6.
%C A244300 Also the number of ballot sequences of length n such that the multiplicities of the largest and the smallest value differ by 6.
%H A244300 Alois P. Heinz, <a href="/A244300/b244300.txt">Table of n, a(n) for n = 8..100</a>
%p A244300 h:= proc(l) local n; n:=nops(l); add(i, i=l)!/mul(mul(1+l[i]-j+
%p A244300     add(`if`(l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n) end:
%p A244300 g:= proc(n, i, l) local j; `if`(n=0 or i<1, 0, `if`(l<>[] and
%p A244300       l[1]-i=6, `if`(irem(n, i, 'j')=0, h([l[], i$j]), 0),
%p A244300       add(g(n-i*j, i-1, [l[], i$j]), j=0..n/i)))
%p A244300     end:
%p A244300 a:= n-> g(n$2, []):
%p A244300 seq(a(n), n=8..35);
%Y A244300 Column k=6 of A238707.
%K A244300 nonn
%O A244300 8,1
%A A244300 _Joerg Arndt_ and _Alois P. Heinz_, Jun 25 2014