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A321278 One half of the sum over all permutations of [n] of the squared difference between the length of the longest increasing subsequence and the length of the longest decreasing subsequence. 7
0, 1, 4, 18, 105, 699, 5285, 45128, 431223, 4540775, 52268029, 653096124, 8810538490, 127622293057, 1975379879871, 32537074533872, 568268861724191, 10490690233451583, 204118868130889733, 4174977363687339452, 89554055679215605982, 2010207472655266461533 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
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
Sequence in context: A231274 A051827 A007711 * A020114 A354015 A009597
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 01 2018
STATUS
approved

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Last modified June 20 22:01 EDT 2024. Contains 373532 sequences. (Running on oeis4.)