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%I #20 Aug 02 2017 23:52:44
%S 0,1,21,182,910,3255,9331,22876,49932,99645,185185,324786,542906,
%T 871507,1351455,2034040,2982616,4274361,6002157,8276590,11228070,
%U 15009071,19796491,25794132,33235300,42385525,53545401,67053546
%N Mean of first six positive powers of n, i.e., (n + n^2 + n^3 + n^4 + n^5 + n^6)/6.
%H Harry J. Smith, <a href="/A059721/b059721.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F a(n) = (n^7 - n)/(6n - 6) = A053700(n)*n/6.
%F G.f.: x*(1+14*x+56*x^2+42*x^3+7*x^4)/(1-x)^7. [_Colin Barker_, May 08 2012]
%e a(2) = (2 + 4 + 8 + 16 + 32 + 64)/6 = 126/6 = 21.
%t Table[Total[n^Range[6]]/6,{n,0,30}] (* _Harvey P. Dale_, Jan 29 2011 *)
%o (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
%Y Cf. A059722, A059723.
%K nonn,easy
%O 0,3
%A _Henry Bottomley_, Feb 07 2001
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