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 A358164 #15 Oct 15 2023 09:27:07
%S A358164 1,1,26,2704,698568,384890688,378771904512,597991783196160,
%T A358164 1450380828625459200,5077825865646165964800,24487520383436615392204800
%N A358164 a(n) is the hafnian of the 2n X 2n symmetric matrix defined by M[i,j] = i*j - ceiling(i*j/3).
%C A358164 The matrix M(n) is the n-th principal submatrix of the rectangular array A143979.
%H A358164 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hafnian">Hafnian</a>
%H A358164 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_matrix">Symmetric matrix</a>
%e A358164 a(2) = 26:
%e A358164 0 1 2 2
%e A358164 1 2 4 5
%e A358164 2 4 6 8
%e A358164 2 5 8 10
%t A358164 M[i_, j_, n_]:=Part[Part[Table[r*c-Ceiling[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 A358164 (PARI) tm(n) = matrix(n, n, i, j, i*j - ceil((i*j)/3));
%o A358164 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 A358164 Cf. A143979.
%Y A358164 Cf. A030511 (matrix element M[n-1,n-1]), A358163 (permanent of M(n)).
%K A358164 nonn,hard,more
%O A358164 0,3
%A A358164 _Stefano Spezia_, Nov 01 2022
%E A358164 a(6) from _Michel Marcus_, May 02 2023
%E A358164 a(7)-a(10) from _Pontus von Brömssen_, Oct 15 2023