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A000584 5th powers: a(n) = n^5.
(Formerly M5231 N2277)
68
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. [From 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

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 to sequences with 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

MAPLE

a:=n->add(add(n^3, j=1..n), k=1..n): seq(a(n), n=0..29); # Zerinvary Lajos, May 09 2007

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 */

CROSSREFS

Partial sums give A000539.

Cf. A000012, A001477, A000290, A000578, A000583, A000539, A062392, A022521 (first differences).

Cf. A162624.

Sequence in context: A017674 A184979 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

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Last modified August 22 03:58 EDT 2014. Contains 245921 sequences.