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 A059721 Mean of first six positive powers of n, i.e., (n + n^2 + n^3 + n^4 + n^5 + n^6)/6. 7
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 21 13:19 EDT 2024. Contains 373544 sequences. (Running on oeis4.)