A059721 Mean of first six positive powers of n, i.e., (n + n^2 + n^3 + n^4 + n^5 + n^6)/6.

0, 1, 21, 182, 910, 3255, 9331, 22876, 49932, 99645, 185185, 324786, 542906, 871507, 1351455, 2034040, 2982616, 4274361, 6002157, 8276590, 11228070, 15009071, 19796491, 25794132, 33235300, 42385525, 53545401, 67053546

Offset

0,3

Links

Harry J. Smith, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

a(n) = (n^7 - n)/(6n - 6) = A053700(n)*n/6.

G.f.: x*(1+14*x+56*x^2+42*x^3+7*x^4)/(1-x)^7. [Colin Barker, May 08 2012]

Example

a(2) = (2 + 4 + 8 + 16 + 32 + 64)/6 = 126/6 = 21.

Mathematica

Table[Total[n^Range[6]]/6, {n, 0, 30}]  (* Harvey P. Dale, Jan 29 2011 *)

Prog

(PARI) { for (n=0, 1000, if (n==1, a=1, a=(n^7 - n)/(6*n - 6)); write("b059721.txt", n, " ", a); ) } \\ Harry J. Smith, Jun 28 2009

Crossrefs

Cf. A059722, A059723.

Sequence in context: A025604 A219412 A062159 * A054370 A219171 A232045

Adjacent sequences: A059718 A059719 A059720 * A059722 A059723 A059724

Keyword

nonn,easy

Author

Henry Bottomley, Feb 07 2001

Status

approved