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A321315
Number of permutations of [n] where the length of the longest increasing subsequence is larger than or equal to the length of the longest decreasing subsequence.
4
1, 1, 5, 14, 78, 488, 3161, 25092, 231428, 2299664, 24809824, 296046900, 3863542365, 54081895706, 806425921874, 12828011279528, 217574673205512, 3914918953508792, 74300528009315864, 1482219340166034896, 31035891175182089248, 681299189806864371412, 15649118660372502746968
OFFSET
1,3
FORMULA
a(n) = Sum_{k=0..n-1} A321316(n,k).
a(n) = A321313(n) + A321314(n).
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);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 03 2018
STATUS
approved