A002594 a(n) = n^2*(16*n^4-20*n^2+7)/3.

1, 244, 3369, 20176, 79225, 240276, 611569, 1370944, 2790801, 5266900, 9351001, 15787344, 25552969, 39901876, 60413025, 89042176, 128177569, 180699444, 250043401, 340267600, 456123801, 603132244, 787660369, 1017005376, 1299480625, 1644505876, 2062701369, 2565985744, 3167677801, 3882602100, 4727198401, 5719634944, 6879925569, 8230050676

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

It is possible that the Croxton and Crowden reference gives a better explanation than the simple formula in the new definition.

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).

Crossrefs

Cf. A000539, A016757.

Programs

Magma

[n^2/3 * (16*n^4 - 20*n^2 + 7): n in [1..40]]; // Vincenzo Librandi, Sep 07 2011

Maple

A002594:=-(z+1)*(z**4+236*z**3+1446*z**2+236*z+1)/(z-1)**7; # Simon Plouffe in his 1992 dissertation

Formula

G.f.: x*(1+x)*(1+236*x+1446*x^2+236*x^3+x^4)/(1-x)^7. [Simon Plouffe]

Extensions

The old definition was wrong, entry revised by N. J. A. Sloane, Jun 10 2012