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, 83289682, 102677835, 125689655, 152847856
Offset: 0
Examples
a(2) = (2 + 4 + 8 + 16 + 32 + 64)/6 = 126/6 = 21.
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).
Programs
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Mathematica
Table[Total[n^Range[6]]/6,{n,0,30}] (* Harvey P. Dale, Jan 29 2011 *) -
PARI
a(n) = { if(n==1, 1, (n^7 - n)/(6*n - 6)) } \\ Harry J. Smith, Jun 28 2009
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]