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

0,3

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.

Links

Table of n, a(n) for n=0..7.

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001477, A000217, A059721.

Sequence in context: A217091 A144173 A127343 * A108496 A185430 A221263

Adjacent sequences: A108045 A108046 A108047 * A108049 A108050 A108051

Keyword

nonn

Author

Henry Bottomley, Jun 01 2005

Status

approved