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 A074351 #28 Jul 02 2018 22:37:49
%S A074351 1,1,2,6,24,240,720,5040,40320,514080,3628800,80166240,479001600,
%T A074351 6797831040,93774320640,1307674368000,20922789888000,523845011289600,
%U A074351 6402373705728000,153101632051630080,2471368711740364800,51182316789956352000,1124000727777607680000
%N A074351 Number of elements of S_n having order n.
%C A074351 If n is a prime power then a(n) = (n-1)!. - _Vladeta Jovovic_, Sep 29 2002
%H A074351 Alois P. Heinz, <a href="/A074351/b074351.txt">Table of n, a(n) for n = 1..450</a> (first 100 terms from T. D. Noe)
%H A074351 J. Kuzmanovich and A. Pavlichenkov, <a href="http://www.jstor.org/stable/2695329">Finite groups of matrices whose entries are integers</a>, Amer. Math. Monthly, 109 (2002), 173-186.
%F A074351 n!/(a_1!*a_2!*...*a_d!*k_1^a_1*k_2^a_2*...*k_d^a_d) is the number of elements of S_n having order n that are permutations with distinct cycle-lengths k_1, ..., k_d having multiplicities a_1, ..., a_d, where lcm(k_1, ..., k_d)=n. Summing over all permutation types gives the total.
%F A074351 a(n) = n!*coefficient of x^n in expansion of Sum_{i divides n} mu(n/i)*exp(Sum_{j divides i} x^j/j). - _Vladeta Jovovic_, Sep 29 2002
%e A074351 a(10) = 514080 because {10}, {5, 2, 2, 1} and {5, 2, 1, 1, 1} are the unique multisets of cycle lengths summing to 10 whose lcm is 10 and 10!/(1!*10^1) + 10!/(1!*2!*1!*5^1*2^2*1^1) + 10!/(1!*1!*3!*5^1*2^1*1^3) = 514080.
%t A074351 a[n_] := SeriesCoefficient[ Series[ Sum[ MoebiusMu[n/i]*Exp[Sum[x^j/j, {j, Divisors[i]}]], {i, Divisors[n]}], {x, 0, n}], n]*n!; Table[a[n], {n, 1, 21}] (* _Jean-François Alcover_, May 21 2012, after _Vladeta Jovovic_ *)
%o A074351 (PARI) a(n)={n!*polcoeff(sumdiv(n, i, moebius(n/i)*exp(sumdiv(i, j, x^j/j) + O(x*x^n))), n)} \\ _Andrew Howroyd_, Jul 02 2018
%Y A074351 Cf. A001189, A074859, A290961 (the same for endofunctions).
%Y A074351 Main diagonal of A057731.
%K A074351 nice,easy,nonn
%O A074351 1,3
%A A074351 K Murray Peebles (m.peebles(AT)sms.ed.ac.uk), Sep 26 2002