OFFSET
1,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..80
Wikipedia, Longest increasing subsequence
FORMULA
a(n) = (1/2) * Sum_{k=1-n..n-1} k^2 * A321316(n,k).
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))^2/2:
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