A321276 Sum over all permutations of [n] of the length of the longest increasing subsequence raised to the power of the length of the longest decreasing subsequence.

1, 3, 20, 174, 1915, 25861, 407691, 7330188, 148016449, 3312032213, 81207824255, 2162810487154, 62125097028962, 1913156511113517, 62839800627095263, 2191735865280260976, 80859575674731497805, 3144804693463679033629, 128550453029684197431607

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..70

Wikipedia, Longest increasing subsequence

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*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);

Crossrefs

Cf. A003316, A321273, A321274, A321275, A321277, A321278.

Sequence in context: A216583 A354018 A154644 * A000891 A242164 A129840

Adjacent sequences: A321273 A321274 A321275 * A321277 A321278 A321279

Keyword

nonn

Author

Alois P. Heinz, Nov 01 2018

Status

approved