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A321277 One half of the sum over all permutations of [n] of the absolute difference between the length of the longest increasing subsequence and the length of the longest decreasing subsequence. 7
0, 1, 2, 12, 61, 367, 2805, 23372, 213317, 2189823, 24882811, 305633678, 4037554628, 57447084699, 877263905683, 14276260437624, 246201450585329, 4487236144246511, 86286209907252739, 1746559569805617910, 37106502447954647906, 825196425771658993531 (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} abs(k) * 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*abs(l[1]-nops(l))/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, A321278, A321316.

Sequence in context: A127044 A245091 A037562 * A187001 A125831 A121177

Adjacent sequences:  A321274 A321275 A321276 * A321278 A321279 A321280

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 01 2018

STATUS

approved

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Last modified November 14 20:11 EST 2019. Contains 329129 sequences. (Running on oeis4.)