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A245665 Number of permutations of length n with longest increasing subsequence of length 9.

%I A245665 #7 Jul 28 2014 18:17:45
%S A245665 1,81,3961,153341,5213287,164060352,4927007100,143938455225,
%T A245665 4142847526101,118504614869214,3389618010035458,97376389179852540,
%U A245665 2818543211543628620,82388635477750176388,2436180769576352799396,72958306889459609898731,2214789502139053994814716
%N A245665 Number of permutations of length n with longest increasing subsequence of length 9.
%H A245665 Alois P. Heinz, <a href="/A245665/b245665.txt">Table of n, a(n) for n = 9..60</a>
%p A245665 h:= proc(l) local n; n:= nops(l); add(i, i=l)! /mul(mul(1+l[i]-j
%p A245665     +add(`if`(l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n) end:
%p A245665 g:= (n, i, l)-> `if`(n=0 or i=1, h([l[], 1$n])^2, `if`(i<1, 0,
%p A245665                 add(g(n-i*j, i-1, [l[], i$j]), j=0..n/i))):
%p A245665 a:= n-> g(n-9, min(n-9, 9), [9]):
%p A245665 seq(a(n), n=9..30);
%Y A245665 Column k=9 of A047874.
%K A245665 nonn
%O A245665 9,2
%A A245665 _Alois P. Heinz_, Jul 28 2014