A217676 - OEIS

%I #7 Nov 01 2014 22:30:15

%S 1,82,4062,159404,5497718,175652924,5360393100,159281625000,

%T 4667810722500,136102249609224,3973117419487320,116645785269445696,

%U 3455520662446396976,103544836992023092832,3144187412886704149472,96883566754646092037696,3032518386648514382974097

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

%H Alois P. Heinz, <a href="/A217676/b217676.txt">Table of n, a(n) for n = 9..200</a>

%F a(n) = A214152(n,9) = A000142(n)-A072132(n) = A000142(n)-A214015(n,8).

%e a(9) = 1: 123456789.

%p b:= proc(n) option remember; `if`(n<4, n!,

%p       (-147456*(n+4)*(n-1)^2*(n-2)^2*(n-3)^2*b(n-4)

%p       +128*(33876+30709*n+6687*n^2+410*n^3)*(n-1)^2*(n-2)^2*b(n-3)

%p       -4*(1092*n^5+37140*n^4+455667*n^3+2387171*n^2+4649270*n+1206000)*

%p       (n-1)^2*b(n-2) +(-17075520+(22488312+(29223280+(10509820+(1764252+

%p       (154164+(6804+120*n)*n)*n)*n)*n)*n)*n)*b(n-1))/

%p       ((n+16)*(n+7)^2*(n+15)^2*(n+12)^2))

%p     end:

%p a:= n-> n! -b(n):

%p seq(a(n), n=9..30);

%Y Cf. A000142, A072132, A214015, A214152.

%K nonn

%O 9,2

%A _Alois P. Heinz_, Oct 10 2012