cp's OEIS Frontend

A217675 Number of permutations in S_n containing an increasing subsequence of length 8.

%I A217675 #7 Nov 01 2014 22:29:45
%S A217675 1,65,2603,83923,2410291,64864819,1683724308,42918747000,
%T A217675 1086997811325,27571922195325,704311698875426,18189847735254134,
%U A217675 476311846323448840,12672229166094171240,343069245941729668380,9461927811882316662636,266091066751920438364275
%N A217675 Number of permutations in S_n containing an increasing subsequence of length 8.
%H A217675 Alois P. Heinz, <a href="/A217675/b217675.txt">Table of n, a(n) for n = 8..200</a>
%F A217675 a(n) = A214152(n,8) = A000142(n)-A072131(n) = A000142(n)-A214015(n,7).
%e A217675 a(8) = 1: 12345678.
%p A217675 b:= proc(n) option remember; `if`(n<8, n!, ((-343035+429858*n
%p A217675        +238440*n^3+38958*n^4+634756*n^2+2940*n^5+84*n^6)*b(n-1)
%p A217675        -(1974*n^4+36336*n^3+213240*n^2+407840*n+82425)*(n-1)^2*b(n-2)
%p A217675        +2*(49875+42646*n+6458*n^2)*(n-1)^2*(n-2)^2*b(n-3)
%p A217675        -11025*(n-1)^2*(n-2)^2*(n-3)^2*b(n-4))/ ((n+6)^2*(n+10)^2*(n+12)^2))
%p A217675     end:
%p A217675 a:= n-> n! -b(n):
%p A217675 seq(a(n), n=8..25);
%Y A217675 Cf. A000142, A072131, A214015, A214152.
%K A217675 nonn
%O A217675 8,2
%A A217675 _Alois P. Heinz_, Oct 10 2012