This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A358160 #13 Oct 15 2023 09:26:55
%S A358160 1,2,40,3884,1016376,534983256,510252517152,802452895865280,
%T A358160 1901953775079849600,6537796866589765507200,31381746234057256630521600
%N A358160 a(n) is the hafnian of the 2n X 2n symmetric matrix defined by M[i,j] = i*j - floor(i*j/3).
%C A358160 The matrix M(n) is the n-th principal submatrix of the rectangular array A143976.
%H A358160 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hafnian">Hafnian</a>
%H A358160 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_matrix">Symmetric matrix</a>
%e A358160 a(2) = 40:
%e A358160 1 2 2 3
%e A358160 2 3 4 6
%e A358160 2 4 6 8
%e A358160 3 6 8 11
%t A358160 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]
%o A358160 (PARI) tm(n) = matrix(n, n, i, j, i*j - (i*j)\3);
%o A358160 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
%Y A358160 Cf. A143976.
%Y A358160 Cf. A071619 (matrix element M[n,n]), A358159 (permanent of M(2*n)), A358042 (trace of M(n)).
%K A358160 nonn,hard,more
%O A358160 0,2
%A A358160 _Stefano Spezia_, Nov 01 2022
%E A358160 a(6) from _Michel Marcus_, May 02 2023
%E A358160 a(7)-a(10) from _Pontus von Brömssen_, Oct 15 2023