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 A305730 #50 Jun 25 2018 15:26:59
%S A305730 0,0,2,8,60,440,3710,34608,355992,4004880,48948570,646121080,
%T A305730 9163171732,138974771208,2244977073430,38485321258720,697867158824880,
%U A305730 13346709412525728,268504389357870642,5668425997555046760,125302048367006296940,2894477317277845459160
%N A305730 a(n) is the total displacement of all letters in all permutations of n letters with no fixed points.
%H A305730 Seiichi Manyama, <a href="/A305730/b305730.txt">Table of n, a(n) for n = 0..400</a>
%F A305730 a(n) = n * (n+1) * A000166(n)/3 = 2/3 * A065087(n).
%F A305730 a(n) = n * (n+1)!/3 * Sum_{k=0..n} (-1)^k/k!.
%F A305730 a(n) = n * (n+1) * (a(n-1)/(n-1) + (-1)^n/3) for n > 1.
%F A305730 a(n) = 2 * A000313(n+2). - _Alois P. Heinz_, Jun 22 2018
%F A305730 E.g.f.: exp(-x)*x^2*(3 - 2*x + x^2)/(3*(1 - x)^3). - _Ilya Gutkovskiy_, Jun 25 2018
%e A305730 n | 1 2 3 4 | the displacement of all letters | a(n)
%e A305730 --+---------+---------------------------------+------
%e A305730 2 | 2 1 | 1 + 1 = 2 | 2
%e A305730 3 | 2 3 1 | 1 + 1 + 2 = 4 | 8
%e A305730 | 3 1 2 | 2 + 1 + 1 = 4 |
%e A305730 4 | 2 1 4 3 | 1 + 1 + 1 + 1 = 4 | 60
%e A305730 | 2 3 4 1 | 1 + 1 + 1 + 3 = 6 |
%e A305730 | 2 4 1 3 | 1 + 2 + 2 + 1 = 6 |
%e A305730 | 3 1 4 2 | 2 + 1 + 1 + 2 = 6 |
%e A305730 | 3 4 1 2 | 2 + 2 + 2 + 2 = 8 |
%e A305730 | 3 4 2 1 | 2 + 2 + 1 + 3 = 8 |
%e A305730 | 4 1 2 3 | 3 + 1 + 1 + 1 = 6 |
%e A305730 | 4 3 1 2 | 3 + 1 + 2 + 2 = 8 |
%e A305730 | 4 3 2 1 | 3 + 1 + 1 + 3 = 8 |
%o A305730 (PARI) {a(n) = n*(n+1)!/3*sum(k=0, n, (-1)^k/k!)}
%Y A305730 Cf. A000166, A000313, A065087, A090672.
%K A305730 nonn
%O A305730 0,3
%A A305730 _Seiichi Manyama_, Jun 22 2018