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 A357420 #14 Oct 16 2023 11:49:09
%S A357420 1,1,1,8,86,878,13730,348760,11622396,509566864,26894616012,
%T A357420 1701189027944,125492778658096,10738546182981256,1049631636279244832,
%U A357420 117756049412699967072
%N A357420 a(n) is the hafnian of the 2n X 2n symmetric matrix defined by M[i,j] = abs(i - j) if min(i, j) < max(i, j) <= 2*min(i, j), and otherwise 0.
%H A357420 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hafnian">Hafnian</a>
%H A357420 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_matrix">Symmetric matrix</a>
%e A357420 a(4) = 86:
%e A357420 0, 1, 0, 0, 0, 0, 0, 0;
%e A357420 1, 0, 1, 2, 0, 0, 0, 0;
%e A357420 0, 1, 0, 1, 2, 3, 0, 0;
%e A357420 0, 2, 1, 0, 1, 2, 3, 4;
%e A357420 0, 0, 2, 1, 0, 1, 2, 3;
%e A357420 0, 0, 3, 2, 1, 0, 1, 2;
%e A357420 0, 0, 0, 3, 2, 1, 0, 1;
%e A357420 0, 0, 0, 4, 3, 2, 1, 0.
%t A357420 M[i_, j_, n_] := If[Min[i, j] < Max[i, j] <= 2 Min[i, j], Abs[j - i], 0]; a[n_] := Sum[Product[M[Part[PermutationList[s, 2 n], 2 i - 1], Part[PermutationList[s, 2 n], 2 i], 2 n], {i, n}], {s, SymmetricGroup[2 n] // GroupElements}]/(n!*2^n); Array[a, 6, 0]
%Y A357420 Cf. A000982 (number of zero matrix elements of M(n)), A003983, A007590 (number of positive matrix elements of M(n)), A049581, A051125, A352967, A353452 (determinant of M(n)), A353453 (permanent of M(n)).
%Y A357420 Cf. A202038, A336114, A336286, A336400, A338456.
%Y A357420 Cf. A356481, A356482, A356483, A356484, A357279.
%K A357420 nonn,hard,more
%O A357420 0,4
%A A357420 _Stefano Spezia_, Sep 27 2022
%E A357420 a(6)-a(15) from _Pontus von Brömssen_, Oct 16 2023