A244304 - OEIS

%I #5 Jun 26 2014 14:45:39

%S 11,66,923,6761,59631,430135,3286934,22973870,166443706,1140859011,

%T 8005160811,54582972124,377341672273,2571480311931,17687177703846,

%U 120864485062762,832211596826779,5716894541334650,39541329587796481,273544962791156596,1904469339140619197

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

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

%H Alois P. Heinz, <a href="/A244304/b244304.txt">Table of n, a(n) for n = 12..80</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=10, `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=12..35);

%Y Column k=10 of A238707.

%K nonn

%O 12,1

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