A002594 a(n) = n^2*(16*n^4-20*n^2+7)/3. (Formerly M5421 N2354)

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

1,2

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

Cf. A000539, A016757.

Sequence in context: A262092 A178266 A081864 * A194134 A085440 A218246

Adjacent sequences: A002591 A002592 A002593 * A002595 A002596 A002597

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