Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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