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A321274 Sum over all permutations of [n] of the minimum of the lengths of longest increasing subsequence and longest decreasing subsequence.

%I A321274 #14 Nov 02 2018 21:35:24
%S A321274 1,2,10,46,274,1894,14660,128648,1259740,13540882,158689006,
%T A321274 2018664332,27699652406,407457326286,6395402111042,106731605965344,
%U A321274 1887716456363316,35269257369001618,694027051724655398,14346767204627002964,310852440258761877068,7045172291061429434354
%N A321274 Sum over all permutations of [n] of the minimum of the lengths of longest increasing subsequence and longest decreasing subsequence.
%H A321274 Alois P. Heinz, <a href="/A321274/b321274.txt">Table of n, a(n) for n = 1..70</a>
%H A321274 Wikipedia, <a href="https://en.wikipedia.org/wiki/Longest_increasing_subsequence">Longest increasing subsequence</a>
%F A321274 a(n) < A003316(n) < A321273(n) for n > 1.
%p A321274 h:= l-> (n-> add(i, i=l)!/mul(mul(1+l[i]-j+add(`if`(j>
%p A321274     l[k], 0, 1), k=i+1..n), j=1..l[i]), i=1..n))(nops(l)):
%p A321274 f:= l-> h(l)^2*min(l[1], nops(l)):
%p A321274 g:= (n, i, l)-> `if`(n=0 or i=1, f([l[], 1$n]),
%p A321274      g(n, i-1, l) +g(n-i, min(i, n-i), [l[], i])):
%p A321274 a:= n-> g(n$2, []):
%p A321274 seq(a(n), n=1..23);
%Y A321274 Cf. A003316, A321273, A321275, A321276, A321277, A321278.
%K A321274 nonn
%O A321274 1,2
%A A321274 _Alois P. Heinz_, Nov 01 2018