cp's OEIS Frontend

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

%I A002594 M5421 N2354 #45 Jul 08 2025 00:16:50
%S A002594 1,244,3369,20176,79225,240276,611569,1370944,2790801,5266900,9351001,
%T A002594 15787344,25552969,39901876,60413025,89042176,128177569,180699444,
%U A002594 250043401,340267600,456123801,603132244,787660369,1017005376,1299480625,1644505876,2062701369,2565985744,3167677801,3882602100,4727198401,5719634944,6879925569,8230050676
%N A002594 a(n) = n^2*(16*n^4-20*n^2+7)/3.
%C A002594 It is possible that the Croxton and Crowden reference gives a better explanation than the simple formula in the new definition.
%C A002594 Sum of the fifth powers of the first n odd numbers. - _Michel Marcus_, Dec 01 2015
%D A002594 F. E. Croxton and D. J. Cowden, Applied General Statistics. 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 1955, p. 742.
%D A002594 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002594 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002594 Vincenzo Librandi, <a href="/A002594/b002594.txt">Table of n, a(n) for n = 1..10000</a>
%H A002594 F. E. Croxton and D. J. Cowden, <a href="/A000447/a000447.pdf">Applied General Statistics</a>, 2nd Ed., Prentice-Hall, Englewood Cliffs, NJ, 1955 [Annotated scans of just pages 742-743]
%H A002594 Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H A002594 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H A002594 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A002594 G.f.: x*(1+x)*(1+236*x+1446*x^2+236*x^3+x^4)/(1-x)^7. [_Simon Plouffe_]
%p A002594 A002594:=-(z+1)*(z**4+236*z**3+1446*z**2+236*z+1)/(z-1)**7; # _Simon Plouffe_ in his 1992 dissertation
%o A002594 (Magma) [n^2/3 * (16*n^4 - 20*n^2 + 7): n in [1..40]]; // _Vincenzo Librandi_, Sep 07 2011
%Y A002594 Cf. A000539, A016757.
%K A002594 nonn,easy
%O A002594 1,2
%A A002594 _N. J. A. Sloane_
%E A002594 The old definition was wrong, entry revised by _N. J. A. Sloane_, Jun 10 2012