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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.
7
1, 2, 10, 46, 274, 1894, 14660, 128648, 1259740, 13540882, 158689006, 2018664332, 27699652406, 407457326286, 6395402111042, 106731605965344, 1887716456363316, 35269257369001618, 694027051724655398, 14346767204627002964, 310852440258761877068, 7045172291061429434354
OFFSET
1,2
FORMULA
a(n) < A003316(n) < A321273(n) for n > 1.
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);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 01 2018
STATUS
approved