OFFSET
0,2
COMMENTS
The matrix M(n) is the n-th principal submatrix of the rectangular array A143976.
LINKS
EXAMPLE
a(2) = 40:
1 2 2 3
2 3 4 6
2 4 6 8
3 6 8 11
MATHEMATICA
M[i_, j_, n_]:=Part[Part[Table[r*c-Floor[r*c/3], {r, n}, {c, n}], i], j]; a[n_]:=Sum[Product[M[Part[PermutationList[s, 2n], 2i-1], Part[PermutationList[s, 2n], 2i], 2n], {i, n}], {s, SymmetricGroup[2n]//GroupElements}]/(n!*2^n); Array[a, 6, 0]
PROG
(PARI) tm(n) = matrix(n, n, i, j, i*j - (i*j)\3);
a(n) = my(m = tm(2*n), s=0); forperm([1..2*n], p, s += prod(j=1, n, m[p[2*j-1], p[2*j]]); ); s/(n!*2^n); \\ Michel Marcus, May 02 2023
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Stefano Spezia, Nov 01 2022
EXTENSIONS
a(6) from Michel Marcus, May 02 2023
a(7)-a(10) from Pontus von Brömssen, Oct 15 2023
STATUS
approved