A347767 - OEIS

A347767

Irregular table read by rows, T(n, k) is the rank of the k-th negative Euler permutation of {1,...,n}, permutations sorted in lexicographical order. If no such permutation exists, then T(n, 0) = 0 by convention.

0, 0, 1, 0, 2, 7, 4, 5, 6, 7, 10, 12, 19, 20, 27, 31, 33, 43, 44, 47, 49, 52, 54, 56, 59, 69, 73, 78, 80, 83, 86, 87, 89, 93, 1, 3, 4, 5, 17, 18, 22, 23, 24, 25, 27, 28, 29, 37, 38, 42, 43, 46, 48, 51, 52, 53, 56, 58, 61, 62, 66, 67, 72, 100, 101, 102, 103, 106

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OFFSET

0,5

COMMENTS

Let M be the tangent matrix of dimension n X n. The definition of a tangent matrix is given in A346831. An Euler permutation of order n is a permutation sigma of {1,...,n} if P = Product_{k=1..n} M(k, sigma(k)) does not vanish. We say sigma is a negative Euler permutation of order n if P = -1. See A347601 for further details.

A347766 gives the table of positive Euler permutations. Related sequences are A347599 (Genocchi permutations) and A347600 (Seidel permutations).

LINKS

Table of n, a(n) for n=0..67.

EXAMPLE

Table of negative Euler permutations, length of rows is A347602:

[0] 0;

[1] 0;

[2] 1;

[3] 0;

[4] 2, 7;

[5] 4, 5, 6, 7, 10, 12, 19, 20, 27, 31, 33, 43, 44, 47, 49, ...

The first 8 permutations corresponding to the ranks are for n = 5: