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%I #8 Nov 01 2014 22:27:45
%S 2,6,23,78,207,458,891,1578,2603,4062,6063,8726,12183,16578,22067,
%T 28818,37011,46838,58503,72222,88223,106746,128043,152378,180027,
%U 211278,246431,285798,329703,378482,432483,492066,557603,629478,708087,793838,887151,988458
%N Number of permutations in S_{n+2} containing an increasing subsequence of length n.
%H Alois P. Heinz, <a href="/A217200/b217200.txt">Table of n, a(n) for n = 0..1000</a>
%F a(0) = 2, a(n) = 3+n+n^2/2+n^3+n^4/2 for n>0.
%F G.f.: (x^5-3*x^4+3*x^3+13*x^2-4*x+2)/(1-x)^5.
%e a(2) = 23: only one of 4! = 24 permutations of {1,2,3,4} has no increasing subsequence of length 2: 4321.
%p a:= n-> 3+(2+(1+(n+2)*n)*n)*n/2-`if`(n=0, 1, 0):
%p seq(a(n), n=0..60);
%Y A diagonal of A214152.
%K nonn,easy
%O 0,1
%A _Alois P. Heinz_, Sep 27 2012
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