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A001015
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Seventh powers: a(n) = n^7.
(Formerly M5392 N2341)
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72
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0, 1, 128, 2187, 16384, 78125, 279936, 823543, 2097152, 4782969, 10000000, 19487171, 35831808, 62748517, 105413504, 170859375, 268435456, 410338673, 612220032, 893871739, 1280000000, 1801088541, 2494357888, 3404825447, 4586471424, 6103515625, 8031810176
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OFFSET
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0,3
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COMMENTS
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For n>0, (a(3*n-1)^7-a(2*n-1)^7-a(n)^7)/(7*(3*n-1)*(2*n-1)*n) = (2*A001106(n)+1)^2 (see Barisien reference, problem 173). - Bruno Berselli, Feb 01 2011
Number of the form a(n) + a(n+1) + ... + a(n+k) is never prime for all n, k>=0. This could be proved by the method indicated in the comment in A256581. - Vladimir Shevelev and Peter J. C. Moses, Apr 04 2015
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REFERENCES
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E.-N. Barisien, Supplemento al Periodico di Matematica, Raffaello Giusti Editore (Livorno), July 1913, p. 135 (Problem 173).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n = 0..1000
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
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FORMULA
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Multiplicative with a(p^e) = p^(7e). - David W. Wilson, Aug 01 2001
Totally multiplicative sequence with a(p) = p^7 for primes p. - Jaroslav Krizek, Nov 01 2009
a(n) = 7*a(n-1) - 21* a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) + 5040. - Ant King, Sep 24 2013
a(n) = n + Sum_{j=0..n-1}{k=1..6}binomial(7,k)*j^(7-k). - Patrick J. McNab, Mar 28 2016
G.f.: x*(1+120*x+1191*x^2+2416*x^3+1191*x^4+120*x^5+x^6)/(1-x)^8. See the Maple program. - Wolfdieter Lang, Oct 14 2016
From Kolosov Petro, Oct 22 2018: (Start)
a(n) = Sum_{k=1..n} A300785(n,k).
a(n) = Sum_{k=0..n-1} A300785(n,k). (End)
From Amiram Eldar, Oct 08 2020: (Start)
Sum_{n>=1} 1/a(n) = zeta(7) (A013665).
Sum_{n>=1} (-1)^(n+1)/a(n) = 63*zeta(7)/64 (A275710). (End)
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MAPLE
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A001015:=z*(1191*z^4+120*z^5+1191*z^2+2416*z^3+120*z+z^6+1)/(z-1)^8; # Simon Plouffe in his 1992 dissertation; offset corrected by M. F. Hasler, Feb 01 2011
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MATHEMATICA
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Table[n^7, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Apr 15 2011 *)
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PROG
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(Maxima) makelist(n^7, n, 0, 20); /* Martin Ettl, Jan 15 2013 */
(PARI) a(n)=n^7 \\ Charles R Greathouse IV, Sep 24 2015
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CROSSREFS
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Cf. A000584, A013665, A275710, A300785.
Sequence in context: A250365 A017678 A123253 * A050754 A343287 A113852
Adjacent sequences: A001012 A001013 A001014 * A001016 A001017 A001018
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KEYWORD
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nonn,easy,mult
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from James A. Sellers, Sep 19 2000
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STATUS
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approved
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