

A316775


a(n) is the number of permutations of [1..n] that have the same number of inversions as noninversions.


2



1, 1, 0, 0, 6, 22, 0, 0, 3836, 29228, 0, 0, 25598186, 296643390, 0, 0, 738680521142, 11501573822788, 0, 0, 62119523114983224, 1214967840930909302, 0, 0, 12140037056605135928410, 285899248139692651257566, 0, 0, 4759461354691529363949651814
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OFFSET

0,5


COMMENTS

a(n) is zero when n choose 2 is odd, that is for numbers that have remainders 2 or 3 when divided by 4.


LINKS



FORMULA



EXAMPLE

Consider a permutation 1432. It has exactly three pairs of numbers, the first of them is 1, that are in increasing order. The other three pairs are in decreasing order. The other 5 permutations of size 4 with this property are 2341, 2413, 3142, 3214, 4123. Thus a(4) = 6.


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



