OFFSET
1,2
COMMENTS
Per exhaustive program, written for bases from 2 to 10, the number of permutations pairs, which have the same ratio, equal to A221740(n)/a(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 StackExchange link). Alexander R. Povolotsky, Jan 26 2013
LINKS
FORMULA
a(n) = -4*A023811(n+1)/((-3 + (-1)^n)*n).
MATHEMATICA
Table[-4*(((n + 1)^(n + 1) - (n + 1))/((n + 1) - 1)^2 - 1)/((-3 + (-1)^n)*n), {n, 1, 50}] (* G. C. Greubel, Feb 19 2017 *)
PROG
(Maxima) makelist(-4*(((n+1)^(n+1)-(n+1))/((n+1)-1)^2-1)/((-3+(-1)^n)*n), n, 1, 20); /* Martin Ettl, Jan 25 2013 */
(PARI) for(n=1, 25, print1(-4*(((n + 1)^(n + 1) - (n + 1))/((n + 1) - 1)^2 - 1)/((-3 + (-1)^n)*n), ", ")) \\ G. C. Greubel, Feb 19 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alexander R. Povolotsky, Jan 23 2013
STATUS
approved