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A245666 Number of permutations of length n with longest increasing subsequence of length 10.

%I A245666 #6 Jul 28 2014 18:22:10
%S A245666 1,100,5941,275705,11110464,410474625,14353045401,484748595081,
%T A245666 16029615164446,523952747921310,17044414451764396,554568496974014588,
%U A245666 18113988555378974988,595604303387826752023,19755504320385394380715,662039152774864970449891
%N A245666 Number of permutations of length n with longest increasing subsequence of length 10.
%H A245666 Alois P. Heinz, <a href="/A245666/b245666.txt">Table of n, a(n) for n = 10..60</a>
%p A245666 h:= proc(l) local n; n:= nops(l); add(i, i=l)! /mul(mul(1+l[i]-j
%p A245666     +add(`if`(l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n) end:
%p A245666 g:= (n, i, l)-> `if`(n=0 or i=1, h([l[], 1$n])^2, `if`(i<1, 0,
%p A245666                 add(g(n-i*j, i-1, [l[], i$j]), j=0..n/i))):
%p A245666 a:= n-> g(n-10, min(n-10, 10), [10]):
%p A245666 seq(a(n), n=10..30);
%Y A245666 Column k=10 of A047874.
%K A245666 nonn
%O A245666 10,2
%A A245666 _Alois P. Heinz_, Jul 28 2014