cp's OEIS Frontend

A217676 Number of permutations in S_n containing an increasing subsequence of length 9.

%I A217676 #7 Nov 01 2014 22:30:15
%S A217676 1,82,4062,159404,5497718,175652924,5360393100,159281625000,
%T A217676 4667810722500,136102249609224,3973117419487320,116645785269445696,
%U A217676 3455520662446396976,103544836992023092832,3144187412886704149472,96883566754646092037696,3032518386648514382974097
%N A217676 Number of permutations in S_n containing an increasing subsequence of length 9.
%H A217676 Alois P. Heinz, <a href="/A217676/b217676.txt">Table of n, a(n) for n = 9..200</a>
%F A217676 a(n) = A214152(n,9) = A000142(n)-A072132(n) = A000142(n)-A214015(n,8).
%e A217676 a(9) = 1: 123456789.
%p A217676 b:= proc(n) option remember; `if`(n<4, n!,
%p A217676       (-147456*(n+4)*(n-1)^2*(n-2)^2*(n-3)^2*b(n-4)
%p A217676       +128*(33876+30709*n+6687*n^2+410*n^3)*(n-1)^2*(n-2)^2*b(n-3)
%p A217676       -4*(1092*n^5+37140*n^4+455667*n^3+2387171*n^2+4649270*n+1206000)*
%p A217676       (n-1)^2*b(n-2) +(-17075520+(22488312+(29223280+(10509820+(1764252+
%p A217676       (154164+(6804+120*n)*n)*n)*n)*n)*n)*n)*b(n-1))/
%p A217676       ((n+16)*(n+7)^2*(n+15)^2*(n+12)^2))
%p A217676     end:
%p A217676 a:= n-> n! -b(n):
%p A217676 seq(a(n), n=9..30);
%Y A217676 Cf. A000142, A072132, A214015, A214152.
%K A217676 nonn
%O A217676 9,2
%A A217676 _Alois P. Heinz_, Oct 10 2012