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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 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 Cf. A003316, A321273, A321274, A321275, A321276, A321277, A321316. Sequence in context: A231274 A051827 A007711 * A020114 A354015 A009597 Adjacent sequences: A321275 A321276 A321277 * A321279 A321280 A321281 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.)