A108048 - OEIS

%I #11 Jun 19 2018 19:40:23

%S 0,1,209430786243,3907821040411155686,614057559169335453819010,

%T 6767073673905716055915469215,13749422954239269326919955861621,

%U 8665930063459510313925842272832668

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

%C 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 a(n) = n*(n^42-1)/(42*(n-1)).

%e a(2) = (2 + 4 + 8 + ... + 4398046511104)/42 = 8796093022206/42 = 209430786243.

%t Table[Mean[n^Range[42]],{n,0,10}] (* _Harvey P. Dale_, Jun 19 2018 *)

%o (PARI) a(n) = if (n<2, n, n*(n^42-1)/(42*(n-1))); \\ _Michel Marcus_, Jul 26 2017

%Y Cf. A001477, A000217, A059721.

%K nonn

%O 0,3

%A _Henry Bottomley_, Jun 01 2005