login
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.
6
1, 3, 20, 174, 1915, 25861, 407691, 7330188, 148016449, 3312032213, 81207824255, 2162810487154, 62125097028962, 1913156511113517, 62839800627095263, 2191735865280260976, 80859575674731497805, 3144804693463679033629, 128550453029684197431607
OFFSET
1,2
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 01 2018
STATUS
approved