A324352 Total number of occurrences of 2 in the (signed) displacement sets of all permutations of [n+2] divided by 2!.

0, 1, 5, 28, 179, 1306, 10757, 98932, 1006007, 11214406, 136041329, 1784556808, 25174694723, 380087428618, 6115760751869, 104481070398556, 1888837397941487, 36026457717419662, 723015306101706857, 15230427461356523056, 336009169512596054459

Offset: 0

Author

Alois P. Heinz, Feb 23 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..448
• Wikipedia, Permutation

Crossrefs

Column k=2 of A324362.

Cf. A306234.

Programs

Maple

a:= n-> (k-> -add((-1)^j*binomial(n, j)*(n+k-j)!, j=1..n)/k!)(2):
seq(a(n), n=0..23);

Mathematica

m = 23;
CoefficientList[(1-Exp[-x])/(1-x)^3 + O[x]^(m+1), x]*Range[0, m]! (* Jean-François Alcover, May 03 2021 *)

Formula

E.g.f.: (1-exp(-x))/(1-x)^3.

a(n) = -1/2! * Sum_{j=1..n} (-1)^j * binomial(n,j) * (n+2-j)!.

a(n) = A306234(n+2,2).