This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A324355 #10 May 03 2021 08:21:51 %S A324355 0,1,11,109,1115,12151,142205,1788361,24118967,347811859,5345895929, %T A324355 87298986325,1510075068419,27590646911023,531082929791861, %U A324355 10743610293871681,227906995674679535,5059315590877577131,117308151182930808977,2835988521500605314829 %N A324355 Total number of occurrences of 5 in the (signed) displacement sets of all permutations of [n+5] divided by 5!. %H A324355 Alois P. Heinz, <a href="/A324355/b324355.txt">Table of n, a(n) for n = 0..445</a> %H A324355 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a> %F A324355 E.g.f.: (1-exp(-x))/(1-x)^6. %F A324355 a(n) = -1/5! * Sum_{j=1..n} (-1)^j * binomial(n,j) * (n+5-j)!. %F A324355 a(n) = A306234(n+5,5). %p A324355 a:= n-> (k-> -add((-1)^j*binomial(n, j)*(n+k-j)!, j=1..n)/k!)(5): %p A324355 seq(a(n), n=0..23); %t A324355 m = 23; %t A324355 CoefficientList[(1-Exp[-x])/(1-x)^6 + O[x]^(m+1), x]*Range[0, m]! (* _Jean-François Alcover_, May 03 2021 *) %Y A324355 Column k=5 of A324362. %Y A324355 Cf. A306234. %K A324355 nonn %O A324355 0,3 %A A324355 _Alois P. Heinz_, Feb 23 2019