cp's OEIS Frontend

A244301 Number of standard Young tableaux with n cells such that the lengths of the first and the last row differ by 7.

%I A244301 #5 Jun 26 2014 07:11:01
%S A244301 8,36,395,2166,15365,87515,537860,3043387,18079805,101484440,
%T A244301 590719670,3340021038,19305133044,110029379692,636377579038,
%U A244301 3658493392345,21277586564634,123462793881974,723417146721998,4238255849152496,25044116796884830,148185594856438664
%N A244301 Number of standard Young tableaux with n cells such that the lengths of the first and the last row differ by 7.
%C A244301 Also the number of ballot sequences of length n such that the multiplicities of the largest and the smallest value differ by 7.
%H A244301 Alois P. Heinz, <a href="/A244301/b244301.txt">Table of n, a(n) for n = 9..100</a>
%p A244301 h:= proc(l) local n; n:=nops(l); add(i, i=l)!/mul(mul(1+l[i]-j+
%p A244301     add(`if`(l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n) end:
%p A244301 g:= proc(n, i, l) local j; `if`(n=0 or i<1, 0, `if`(l<>[] and
%p A244301       l[1]-i=7, `if`(irem(n, i, 'j')=0, h([l[], i$j]), 0),
%p A244301       add(g(n-i*j, i-1, [l[], i$j]), j=0..n/i)))
%p A244301     end:
%p A244301 a:= n-> g(n$2, []):
%p A244301 seq(a(n), n=9..35);
%Y A244301 Column k=7 of A238707.
%K A244301 nonn
%O A244301 9,1
%A A244301 _Joerg Arndt_ and _Alois P. Heinz_, Jun 25 2014