A324359 Total number of occurrences of 9 in the (signed) displacement sets of all permutations of [n+9] divided by 9!.

0, 1, 19, 301, 4659, 73651, 1208849, 20736801, 372683159, 7020426511, 138543438429, 2861318625661, 61767341913539, 1391789835244251, 32689488282841529, 799220290375798681, 20312800343333343279, 535995638431063608871, 14665906835087251866389

Offset: 0

Author

Alois P. Heinz, Feb 23 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..443
• Wikipedia, Permutation

Crossrefs

Column k=9 of A324362.

Cf. A306234.

Programs

Magma

[0] cat [(-1/Factorial(9)) * &+[(-1)^j * Binomial(n,j) * Factorial(n+9-j) : j in [1..n]]: n in [1..20]]; // Vincenzo Librandi, Jun 06 2019

Maple

a:= n-> (k-> -add((-1)^j*binomial(n, j)*(n+k-j)!, j=1..n)/k!)(9):
seq(a(n), n=0..23);

Mathematica

Range[0, 20]! CoefficientList[Series[(1 - Exp[-x])/(1 - x)^10, {x, 0, 20}], x] (* Vincenzo Librandi, Jun 06 2019 *)

Formula

E.g.f.: (1-exp(-x))/(1-x)^10.

a(n) = -1/9! * Sum_{j=1..n} (-1)^j * binomial(n,j) * (n+9-j)!.

a(n) = A306234(n+9,9).