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

1, 2, 10, 46, 274, 1894, 14660, 128648, 1259740, 13540882, 158689006, 2018664332, 27699652406, 407457326286, 6395402111042, 106731605965344, 1887716456363316, 35269257369001618, 694027051724655398, 14346767204627002964, 310852440258761877068, 7045172291061429434354

Offset: 1

Author

Alois P. Heinz, Nov 01 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..70
• Wikipedia, Longest increasing subsequence

Crossrefs

Cf. A003316, A321273, A321275, A321276, A321277, A321278.

Programs

Maple

h:= l-> (n-> add(i, i=l)!/mul(mul(1+l[i]-j+add(`if`(j>
    l[k], 0, 1), k=i+1..n), j=1..l[i]), i=1..n))(nops(l)):
f:= l-> h(l)^2*min(l[1], nops(l)):
g:= (n, i, l)-> `if`(n=0 or i=1, f([l[], 1$n]),
     g(n, i-1, l) +g(n-i, min(i, n-i), [l[], i])):
a:= n-> g(n$2, []):
seq(a(n), n=1..23);

Formula

a(n) < A003316(n) < A321273(n) for n > 1.