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%I A324354 #11 May 03 2021 10:09:36
%S A324354 0,1,9,76,679,6576,69299,792926,9812079,130741156,1867777339,
%T A324354 28494131106,462487232519,7959671021576,144813873037539,
%U A324354 2777366346993766,56009230972732639,1184896664408025036,26240470547134420619,607133649024919944266,14649976322598313989879
%N A324354 Total number of occurrences of 4 in the (signed) displacement sets of all permutations of [n+4] divided by 4!.
%H A324354 Alois P. Heinz, <a href="/A324354/b324354.txt">Table of n, a(n) for n = 0..446</a>
%H A324354 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%F A324354 E.g.f.: (1-exp(-x))/(1-x)^5.
%F A324354 a(n) = -1/4! * Sum_{j=1..n} (-1)^j * binomial(n,j) * (n+4-j)!.
%F A324354 a(n) = A306234(n+4,4).
%p A324354 a:= n-> (k-> -add((-1)^j*binomial(n, j)*(n+k-j)!, j=1..n)/k!)(4):
%p A324354 seq(a(n), n=0..23);
%t A324354 m = 23;
%t A324354 CoefficientList[(1-Exp[-x])/(1-x)^5 + O[x]^(m+1), x]*Range[0, m]! (* _Jean-François Alcover_, May 03 2021 *)
%Y A324354 Column k=4 of A324362.
%Y A324354 Cf. A306234.
%K A324354 nonn
%O A324354 0,3
%A A324354 _Alois P. Heinz_, Feb 23 2019

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