A362820 Number of ordered pairs of derangements on [n] that commute.

1, 0, 1, 4, 33, 136, 1825, 10956, 163009, 1575568, 23894721, 280090900, 5410068961, 73066199064, 1483125027553, 25872759745756, 561027082980225, 10796395534986016, 266457543316023169, 5743345672152317988, 152031229968147150241, 3717043193920429157800, 104377807879737865769121

Offset: 0

Author

Andrew Howroyd, May 05 2023

Keywords

• nonn

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

Crossrefs

A053529 is the corresponding sequence for all permutations.

Cf. A000166, A362819.

Programs

PARI

seq(n)=Vec(serlaplace((1 - x)^2*exp(sum(k=1, n, (x^k/k)/(1-x^k) + O(x*x^n)) + x)))

Formula

E.g.f.: (1 - x)^2 * exp(x) * B(x) where B(x) is the e.g.f. of A053529.