A358158 a(n) is the hafnian of the 2n X 2n symmetric matrix defined by M[i,j] = floor(i*j/3).
1, 0, 4, 238, 31992, 9390096, 4755878928, 3802500283680, 4720879431568800, 8379987002639042400, 20346893722025317036800
Offset: 0
Examples
a(2) = 4:
0 0 1 1
0 1 2 2
1 2 3 4
1 2 4 5
Links
- Wikipedia, Hafnian
- Wikipedia, Symmetric matrix
Crossrefs
Programs
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Mathematica
M[i_, j_, n_]:=Part[Part[Table[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] -
PARI
tm(n) = matrix(n, n, 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
Extensions
a(6) from Michel Marcus, May 02 2023
a(7)-a(10) from Pontus von Brömssen, Oct 15 2023
Comments