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 A362820 #12 May 28 2023 22:20:58 %S A362820 1,0,1,4,33,136,1825,10956,163009,1575568,23894721,280090900, %T A362820 5410068961,73066199064,1483125027553,25872759745756,561027082980225, %U A362820 10796395534986016,266457543316023169,5743345672152317988,152031229968147150241,3717043193920429157800,104377807879737865769121 %N A362820 Number of ordered pairs of derangements on [n] that commute. %C A362820 A derangement is a permutation without fixed points. Two permutations x,y commute if x*y = y*x. %H A362820 Andrew Howroyd, <a href="/A362820/b362820.txt">Table of n, a(n) for n = 0..200</a> %F A362820 E.g.f.: (1 - x)^2 * exp(x) * B(x) where B(x) is the e.g.f. of A053529. %o A362820 (PARI) seq(n)=Vec(serlaplace((1 - x)^2*exp(sum(k=1, n, (x^k/k)/(1-x^k) + O(x*x^n)) + x))) %Y A362820 A053529 is the corresponding sequence for all permutations. %Y A362820 Cf. A000166, A362819. %K A362820 nonn %O A362820 0,4 %A A362820 _Andrew Howroyd_, May 05 2023