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 A356483 #16 Oct 14 2023 23:54:38
%S A356483 1,3,55,2999,347391,69702479,22441691645,10776262328919,
%T A356483 7190279422736061,6439969796874334809,7447188585071730451961
%N A356483 a(n) is the hafnian of a symmetric Toeplitz matrix M(2*n) whose first row consists of prime(1), prime(2), ..., prime(2*n).
%H A356483 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hafnian">Hafnian</a>
%H A356483 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_matrix">Symmetric matrix</a>
%H A356483 Wikipedia, <a href="http://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>
%e A356483 a(2) = 55 because the hafnian of
%e A356483 2 3 5 7
%e A356483 3 2 3 5
%e A356483 5 3 2 3
%e A356483 7 5 3 2
%e A356483 equals M_{1,2}*M_{3,4} + M_{1,3}*M_{2,4} + M_{1,4}*M_{2,3} = 55.
%t A356483 k[i_]:=Prime[i]; M[i_, j_, n_]:=Part[Part[ToeplitzMatrix[Array[k, 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 A356483 (PARI) tm(n) = my(m = matrix(n, n, i, j, if (i==1, prime(j), if (j==1, prime(i))))); for (i=2, n, for (j=2, n, m[i, j] = m[i-1, j-1]; ); ); m;
%o A356483 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 A356483 Cf. A202038, A336114, A336286, A336400, A338456.
%Y A356483 Cf. A356481, A356482, A356484.
%Y A356483 Cf. A356490 (determinant of M(n)), A356491 (permanent of M(n)).
%K A356483 nonn,hard,more
%O A356483 0,2
%A A356483 _Stefano Spezia_, Aug 09 2022
%E A356483 a(6) from _Michel Marcus_, May 02 2023
%E A356483 a(7)-a(10) from _Pontus von Brömssen_, Oct 14 2023