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

0, 1, 209430786243, 3907821040411155686, 614057559169335453819010, 6767073673905716055915469215, 13749422954239269326919955861621, 8665930063459510313925842272832668

Offset: 0

Author

Henry Bottomley, Jun 01 2005

Keywords

• nonn

Comments

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.

Examples

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

Crossrefs

Cf. A001477, A000217, A059721.

Programs

Mathematica

Table[Mean[n^Range[42]],{n,0,10}] (* Harvey P. Dale, Jun 19 2018 *)

PARI

a(n) = if (n<2, n, n*(n^42-1)/(42*(n-1))); \\ Michel Marcus, Jul 26 2017

Formula

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