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 A362820 Number of ordered pairs of derangements on [n] that commute. 2
 1, 0, 1, 4, 33, 136, 1825, 10956, 163009, 1575568, 23894721, 280090900, 5410068961, 73066199064, 1483125027553, 25872759745756, 561027082980225, 10796395534986016, 266457543316023169, 5743345672152317988, 152031229968147150241, 3717043193920429157800, 104377807879737865769121 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A derangement is a permutation without fixed points. Two permutations x,y commute if x*y = y*x. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..200 FORMULA E.g.f.: (1 - x)^2 * exp(x) * B(x) where B(x) is the e.g.f. of A053529. PROG (PARI) seq(n)=Vec(serlaplace((1 - x)^2*exp(sum(k=1, n, (x^k/k)/(1-x^k) + O(x*x^n)) + x))) CROSSREFS A053529 is the corresponding sequence for all permutations. Cf. A000166, A362819. Sequence in context: A027169 A152041 A041027 * A364946 A209034 A095671 Adjacent sequences: A362817 A362818 A362819 * A362821 A362822 A362823 KEYWORD nonn AUTHOR Andrew Howroyd, May 05 2023 STATUS approved

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Last modified July 13 01:42 EDT 2024. Contains 374259 sequences. (Running on oeis4.)