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

0,3

Links

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

Wikipedia, Permutation

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).

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 *)

Prog

(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

Crossrefs

Column k=9 of A324362.

Cf. A306234.

Sequence in context: A152591 A051562 A330846 * A074460 A267010 A182460

Adjacent sequences: A324356 A324357 A324358 * A324360 A324361 A324362

Keyword

nonn

Author

Alois P. Heinz, Feb 23 2019

Status

approved