|
%I #7 Nov 01 2014 22:30:49
%S 1,101,6063,284431,11592572,433386000,15343169775,524963196399,
%T 17597634740010,583499409451862,19269396089593156,636977450902768356,
%U 21156201514272916444,708006643310351350076,23925259865186482138965,817728884509460388159381
%N Number of permutations in S_n containing an increasing subsequence of length 10.
%H Alois P. Heinz, <a href="/A217677/b217677.txt">Table of n, a(n) for n = 10..200</a>
%F a(n) = A214152(n,10) = A000142(n)-A072133(n) = A000142(n)-A214015(n,9).
%p b:= proc(n) option remember;
%p `if`(n<5, n!, ((-1110790863+(1520978576+(1772290401+(607308786+
%p (101671498+(9464664+(500874+(14124+165*n)*n)*n)*n)*n)*n)*n)*n)*b(n-1)
%p -(1129886062*n+559908333*n^2+111239576*n^3+10655238*n^4+8778*n^6
%p +491700*n^5 +353895381)*(n-1)^2*b(n-2) +(258011271+234066216*n
%p +58221266*n^2+5463876*n^3 +172810*n^4)*(n-1)^2*(n-2)^2*b(n-3)
%p -9*(4070430+1504292*n+117469*n^2)* (n-1)^2*(n-2)^2*(n-3)^2*b(n-4)
%p +893025*(n-1)^2*(n-2)^2*(n-3)^2*(n-4)^2*b(n-5)) /
%p ((n+20)^2*(n+8)^2*(n+18)^2*(n+14)^2))
%p end:
%p a:= n-> n! -b(n):
%p seq(a(n), n=10..30);
%Y Cf. A000142, A072133, A214015, A214152.
%K nonn
%O 10,2
%A _Alois P. Heinz_, Oct 10 2012
| 