cp's OEIS Frontend

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

%I A324359 #14 Sep 08 2022 08:46:24
%S A324359 0,1,19,301,4659,73651,1208849,20736801,372683159,7020426511,
%T A324359 138543438429,2861318625661,61767341913539,1391789835244251,
%U A324359 32689488282841529,799220290375798681,20312800343333343279,535995638431063608871,14665906835087251866389
%N A324359 Total number of occurrences of 9 in the (signed) displacement sets of all permutations of [n+9] divided by 9!.
%H A324359 Alois P. Heinz, <a href="/A324359/b324359.txt">Table of n, a(n) for n = 0..443</a>
%H A324359 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%F A324359 E.g.f.: (1-exp(-x))/(1-x)^10.
%F A324359 a(n) = -1/9! * Sum_{j=1..n} (-1)^j * binomial(n,j) * (n+9-j)!.
%F A324359 a(n) = A306234(n+9,9).
%p A324359 a:= n-> (k-> -add((-1)^j*binomial(n, j)*(n+k-j)!, j=1..n)/k!)(9):
%p A324359 seq(a(n), n=0..23);
%t A324359 Range[0, 20]! CoefficientList[Series[(1 - Exp[-x])/(1 - x)^10, {x, 0, 20}], x] (* _Vincenzo Librandi_, Jun 06 2019 *)
%o A324359 (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
%Y A324359 Column k=9 of A324362.
%Y A324359 Cf. A306234.
%K A324359 nonn
%O A324359 0,3
%A A324359 _Alois P. Heinz_, Feb 23 2019