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 A362819 #15 May 08 2023 15:33:17
%S A362819 1,1,4,10,52,196,1216,5944,42400,250912,2008576,13815616,122074624,
%T A362819 950640640,9158267392,79258479616,824644235776,7823203807744,
%U A362819 87245790791680,897748312609792,10665239974537216,118040852776093696,1486172381689544704,17572063073426206720,233446797379437248512
%N A362819 Number of ordered pairs of involutions on [n] that commute.
%C A362819 Two involutions x,y on [n] commute if x*y = y*x (i.e. x(y(i)) = y(x(i)) for i in [n]).
%H A362819 Andrew Howroyd, <a href="/A362819/b362819.txt">Table of n, a(n) for n = 0..200</a>
%F A362819 a(n) = Sum_{k=0..floor(n/2)} A000085(n-2*k) * A000898(k) * binomial(n,2*k) * (2*k)! / (k!*2^k).
%F A362819 E.g.f.: exp(x + 3*x^2/2 + x^4/4).
%o A362819 (PARI) b(n,f) = {sum(k=0, n\2, f(k)*binomial(n,2*k)*(2*k)!/(k!*2^k))}
%o A362819 a(n) = {b(n, k->b(n-2*k, j->1)*b(k, j->2^(k-j)))}
%o A362819 (PARI) seq(n)=Vec(serlaplace(exp(x + 3*x^2/2 + x^4/4 + O(x*x^n))))
%Y A362819 Column k=2 of A362824.
%Y A362819 A053529 is the corresponding sequence for all permutations.
%Y A362819 Cf. A000085, A000898, A181162, A362820, A362825.
%K A362819 nonn
%O A362819 0,3
%A A362819 _Andrew Howroyd_, May 05 2023