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%I #7 Feb 15 2016 09:50:23
%S 1,45,1131,23611,461154,8837823,169844455,3307239364,65559881608,
%T 1325285983528,27321430823064,573932303529170,12269791047231748,
%U 266575464412874571,5877527995117635663,131334452330324176828,2970563969803965041900,67935408457473145627500
%N Number of sequences in {1,...,n}^n with longest increasing subsequence of length three.
%H Alois P. Heinz, <a href="/A268870/b268870.txt">Table of n, a(n) for n = 3..700</a>
%F a(n) = A239299(n) - A239295(n).
%e a(3) = 1: 123.
%e a(4) = 45: 1123, 1124, 1134, 1213, 1214, 1223, 1224, 1231, 1232, 1233, 1241, 1242, 1243, 1244, 1314, 1323, 1324, 1334, 1341, 1342, 1343, 1344, 1423, 1424, 1434, 2123, 2124, 2134, 2234, 2314, 2324, 2334, 2341, 2342, 2343, 2344, 2434, 3123, 3124, 3134, 3234, 4123, 4124, 4134, 4234.
%Y Column k=3 of A245667.
%Y Cf. A239295, A239299.
%K nonn,easy
%O 3,2
%A _Alois P. Heinz_, Feb 15 2016