cp's OEIS Frontend

A108048 Mean of first 42 positive powers of n, i.e., (n + n^2 + n^3 + ... + n^42)/42.

%I A108048 #11 Jun 19 2018 19:40:23
%S A108048 0,1,209430786243,3907821040411155686,614057559169335453819010,
%T A108048 6767073673905716055915469215,13749422954239269326919955861621,
%U A108048 8665930063459510313925842272832668
%N A108048 Mean of first 42 positive powers of n, i.e., (n + n^2 + n^3 + ... + n^42)/42.
%C A108048 Similar sequences can be constructed for mean of first powers, giving A001477, for mean of first two powers, giving A000217, and for mean of first six powers, giving A059721. Next similar sequence seems to be for mean of first 1806 powers.
%F A108048 a(n) = n*(n^42-1)/(42*(n-1)).
%e A108048 a(2) = (2 + 4 + 8 + ... + 4398046511104)/42 = 8796093022206/42 = 209430786243.
%t A108048 Table[Mean[n^Range[42]],{n,0,10}] (* _Harvey P. Dale_, Jun 19 2018 *)
%o A108048 (PARI) a(n) = if (n<2, n, n*(n^42-1)/(42*(n-1))); \\ _Michel Marcus_, Jul 26 2017
%Y A108048 Cf. A001477, A000217, A059721.
%K A108048 nonn
%O A108048 0,3
%A A108048 _Henry Bottomley_, Jun 01 2005