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 A321273 Sum over all permutations of [n] of the maximum of the lengths of increasing or decreasing subsequences. 7
 1, 4, 14, 70, 396, 2628, 20270, 175392, 1686374, 17920528, 208454628, 2629931688, 35774761662, 522351495684, 8149929922408, 135284126840592, 2380119357533974, 44243729657494640, 866599471539160876, 17839886344238238784, 385065445154671172880, 8695565142604747421416 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..60 Wikipedia, Longest increasing subsequence FORMULA A321274(n) < A003316(n) < a(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*max(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 Cf. A003316, A321274, A321275, A321276, A321277, A321278. Sequence in context: A049372 A050549 A222980 * A322700 A167144 A159483 Adjacent sequences:  A321270 A321271 A321272 * A321274 A321275 A321276 KEYWORD nonn AUTHOR Alois P. Heinz, Nov 01 2018 STATUS approved

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Last modified February 20 13:20 EST 2020. Contains 332077 sequences. (Running on oeis4.)