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 A221740 #51 Apr 21 2023 13:00:31
%S A221740 1,7,19,293,1493,38127,293479,10593529,109739369,5135610071,
%T A221740 66987982331,3856048810781,60693710471869,4149140360751583,
%U A221740 76519827268721103,6058888636862818097,128138108936443028945,11533996620790579909159
%N A221740 a(n) = -4*((n-1)*(n+1)^(n+1)+1)/(((-1)^n-3)*n^3).
%C A221740 Per exhaustive program, written for bases from 2 to 10, the number of permutations pairs, which have the same ratio, equal to A221740(n)/A221741(n) = (n^2*(n+1)^n - (n+1)^n + 1) / (-n^2 + n*(n+1)^n + (n+1)^n - n - 1), is: {2,2,3,3,5,3,7,5,7,...} for n >= 1 where n = r-1 and r is the base radix. Judging by above sequence it appears that the number of such permutations pairs is related to phi, which is the Euler totient function - according to A039649, A039650, A214288 (see bullet 1 of the analysis in the answer section of the Mathematics StackExchange link). - _Alexander R. Povolotsky_, Jan 26 2013
%H A221740 G. C. Greubel, <a href="/A221740/b221740.txt">Table of n, a(n) for n = 1..385</a>
%H A221740 Mathematics StackExchange, <a href="http://math.stackexchange.com/questions/210578">Permutations (with no duplicates) of decimal base digits 1,2,...,8,9,0</a>.
%H A221740 NMBRTHRY, <a href="http://old.nabble.com/Number-of-specific-permutations-pairs-relates-to-Euler-Phi-totient-function---to34951281.html">Number of specific permutations pairs relates to Euler Phi totient function?</a>
%F A221740 a(n) = -4*A051846(n)/((-3 + (-1)^n)*n).
%F A221740 From _Alexander R. Povolotsky_, Oct 12 2022: (Start)
%F A221740 floor(a(n+1)/A221741(n+1)) = n.
%F A221740 Limit_{n->oo} (a(n)/A221741(n) - floor(a(n)/A221741(n))) = 0. (End)
%t A221740 Table[-4*((n - 1)*(n + 1)^(n + 1) + 1)/(((-1)^n - 3)*n^3), {n,1,50}] (* _G. C. Greubel_, Feb 19 2017 *)
%o A221740 (Maxima) makelist(-4*((n-1)*(n+1)^(n+1)+1)/(((-1)^n-3)*n^3),n,1,20); /* _Martin Ettl_, Jan 25 2013 */
%o A221740 (PARI) for(n=1,25, print1(-4*((n - 1)*(n + 1)^(n + 1) + 1)/(((-1)^n - 3)*n^3), ", ")) \\ _G. C. Greubel_, Feb 19 2017
%Y A221740 Cf. A221741, A051846.
%K A221740 nonn
%O A221740 1,2
%A A221740 _Alexander R. Povolotsky_, Jan 23 2013