OFFSET
1,2
COMMENTS
Sum of the fifth powers of the first n odd numbers. - Michel Marcus, Dec 01 2015
REFERENCES
F. E. Croxton and D. J. Cowden, Applied General Statistics. 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 1955, p. 742.
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
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
F. E. Croxton and D. J. Cowden, Applied General Statistics, 2nd Ed., Prentice-Hall, Englewood Cliffs, NJ, 1955 [Annotated scans of just pages 742-743]
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
G.f.: x*(1+x)*(1+236*x+1446*x^2+236*x^3+x^4)/(1-x)^7. [Simon Plouffe]
MAPLE
A002594:=-(z+1)*(z**4+236*z**3+1446*z**2+236*z+1)/(z-1)**7; # Simon Plouffe in his 1992 dissertation
PROG
(Magma) [n^2/3 * (16*n^4 - 20*n^2 + 7): n in [1..40]]; // Vincenzo Librandi, Sep 07 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane. The old definition was wrong - entry revised by N. J. A. Sloane, Jun 10 2012. It is possible that the Croxton and Crowden reference gives a better explanation than the simple formula in the new definition.
STATUS
approved