cp's OEIS Frontend

A324353 Total number of occurrences of 3 in the (signed) displacement sets of all permutations of [n+3] divided by 3!.

%I A324353 #10 May 03 2021 08:17:31
%S A324353 0,1,7,49,375,3181,29843,307833,3468671,42432445,560365779,7948580377,
%T A324353 120557659247,1947336998829,33378478735475,605158251430681,
%U A324353 11571369420832383,232739737871570173,4912330587789969971,108564708629365952505,2507303342099915104559
%N A324353 Total number of occurrences of 3 in the (signed) displacement sets of all permutations of [n+3] divided by 3!.
%H A324353 Alois P. Heinz, <a href="/A324353/b324353.txt">Table of n, a(n) for n = 0..447</a>
%H A324353 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%F A324353 E.g.f.: (1-exp(-x))/(1-x)^4.
%F A324353 a(n) = -1/3! * Sum_{j=1..n} (-1)^j * binomial(n,j) * (n+3-j)!.
%F A324353 a(n) = A306234(n+3,3).
%p A324353 a:= n-> (k-> -add((-1)^j*binomial(n, j)*(n+k-j)!, j=1..n)/k!)(3):
%p A324353 seq(a(n), n=0..23);
%t A324353 m = 23;
%t A324353 CoefficientList[(1-Exp[-x])/(1-x)^4 + O[x]^(m+1), x]*Range[0, m]! (* _Jean-François Alcover_, May 03 2021 *)
%Y A324353 Column k=3 of A324362.
%Y A324353 Cf. A306234.
%K A324353 nonn
%O A324353 0,3
%A A324353 _Alois P. Heinz_, Feb 23 2019