|
| |
|
|
A000584
|
|
Fifth powers: a(n) = n^5.
(Formerly M5231 N2277)
|
|
124
|
|
|
|
0, 1, 32, 243, 1024, 3125, 7776, 16807, 32768, 59049, 100000, 161051, 248832, 371293, 537824, 759375, 1048576, 1419857, 1889568, 2476099, 3200000, 4084101, 5153632, 6436343, 7962624, 9765625, 11881376, 14348907, 17210368, 20511149
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
Totally multiplicative sequence with a(p) = p^5 for prime p. - Jaroslav Krizek, Nov 01 2009
The binomial transform yields A059338. The inverse binomial transform yields the (finite) 0, 1, 30, 150, 240, 120, the 5th row in A019538 and A131689. - R. J. Mathar, Jan 16 2013
Equals sum of odd numbers from n^2*(n-1)+1 (A100104) to n^2*(n+1)-1 (A003777). - Bruno Berselli, Mar 14 2014
a(n) mod 10 = n mod 10. - Reinhard Zumkeller, May 10 2014
Numbers of the form a(n) + a(n+1) + ... + a(n+k) are nonprime for all n, k>=0; this can be proved by the method indicated in the comment in A256581. - Vladimir Shevelev and Peter J. C. Moses, Apr 04 2015
|
|
|
REFERENCES
|
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).
|
|
|
LINKS
|
Franklin T. Adams-Watters, Table of n, a(n) for n = 0..500
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.
Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1)
|
|
|
FORMULA
|
G.f.: x*(1+26*x+66*x^2+26*x^3+x^4) / (x-1)^6. [Simon Plouffe in his 1992 dissertation]
Multiplicative with a(p^e) = p^(5e). - David W. Wilson, Aug 01 2001.
E.g.f.: exp(x)*(x+15*x^2+25*x^3+10*x^4+x^5). - Geoffrey Critzer, Jun 12 2013
a(n) = 5*a(n-1) - 10* a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) + 120. - Ant King, Sep 23 2013
a(n) = n + Sum_{j=0..n-1}{k=1..4}binomial(5,k)*j^(5-k). - Patrick J. McNab, Mar 28 2016
From Kolosov Petro, Oct 22 2018: (Start)
a(n) = Sum_{k=1..n} A300656(n,k).
a(n) = Sum_{k=0..n-1} A300656(n,k). (End)
|
|
|
MATHEMATICA
|
Range[0, 50]^5 (* Vladimir Joseph Stephan Orlovsky, Feb 20 2011 *)
|
|
|
PROG
|
(Sage) [log(e^(n^5))for n in xrange(0, 30)] /* Zerinvary Lajos, Jun 03 2009 */
(Haskell)
a000584 = (^ 5) -- Reinhard Zumkeller, Nov 11 2012
(Maxima) makelist(n^5, n, 0, 30); /* Martin Ettl, Nov 12 2012 */
(PARI) a(n)=n^5 \\ Charles R Greathouse IV, Jul 28 2015
|
|
|
CROSSREFS
|
Partial sums give A000539.
Cf. A000012, A001477, A000290, A000578, A000583, A062392, A022521 (first differences).
Cf. A162624.
Sequence in context: A184979 A257855 A055014 * A050752 A153159 A113850
Adjacent sequences: A000581 A000582 A000583 * A000585 A000586 A000587
|
|
|
KEYWORD
|
nonn,easy,mult
|
|
|
AUTHOR
|
N. J. A. Sloane
|
|
|
EXTENSIONS
|
More terms from Henry Bottomley, Jun 21 2001
|
|
|
STATUS
|
approved
|
| |
|
|
