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A321313 Number of permutations of [n] with equal lengths of the longest increasing subsequence and the longest decreasing subsequence. 4
1, 0, 4, 4, 36, 256, 1282, 9864, 99976, 970528, 9702848, 113092200, 1500063930, 20985500212, 305177475748, 4733232671056, 79461918315024, 1427464201289584, 26955955609799728, 531536672155429792, 10980840178654738496, 238597651836121062824, 5446220581860028853936 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
a(n) = n! - 2 * A321314(n).
a(n) = A321315(n) - A321314(n).
a(n) = A321316(n,0).
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-> `if`(l[1]=nops(l), h(l)^2, 0):
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);
MATHEMATICA
h[l_] := With[{n = Length[l]}, Total[l]!/Product[Product[1 + l[[i]] - j + Sum[If[j > l[[k]], 0, 1], {k, i + 1, n}], {j, 1, l[[i]]}], {i, 1, n}]];
f[l_] := If[l[[1]] == Length[l], h[l]^2, 0];
g[n_, i_, l_] := If[n == 0 || i == 1, f[Join[l, Table[1, {n}]]], g[n, i - 1, l] + g[n - i, Min[i, n - i], Append[l, i]]];
a[n_] := g[n, n, {}];
Array[a, 25] (* Jean-François Alcover, Aug 31 2021, after Alois P. Heinz *)
CROSSREFS
Column k=0 of A321316.
Sequence in context: A100303 A192348 A111882 * A070959 A367643 A125066
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 03 2018
STATUS
approved

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)