cp's OEIS Frontend

A259322 Sum of sixth powers of odd numbers.

%I A259322 #19 Aug 16 2015 12:04:01
%S A259322 1,730,16355,134004,665445,2437006,7263815,18654440,42792009,89837890,
%T A259322 175604011,323639900,567780525,955201014,1550024335,2437528016,
%U A259322 3728995985,5567261610,8132988019,11651731780,16401836021,22723199070,31026964695
%N A259322 Sum of sixth powers of odd numbers.
%H A259322 Colin Barker, <a href="/A259322/b259322.txt">Table of n, a(n) for n = 1..1000</a>
%H A259322 J. L. Bailey, Jr., <a href="http://dx.doi.org/10.1214/aoms/1177732978">A table to facilitate the fitting of certain logistic curves</a>, Annals Math. Stat., 2 (1931), 355-359.
%H A259322 J. L. Bailey, <a href="/A002309/a002309.pdf">A table to facilitate the fitting of certain logistic curves</a>, Annals Math. Stat., 2 (1931), 355-359. [Annotated scanned copy]
%H A259322 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 A259322 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F A259322 a(n) = (n*(-31+196*n^2-336*n^4+192*n^6))/21. - _Colin Barker_, Jun 29 2015
%F A259322 G.f.: x*(x^6+722*x^5+10543*x^4+23548*x^3+10543*x^2+722*x+1) / (x-1)^8. - _Colin Barker_, Jun 29 2015
%p A259322 f:=n->add((2*i+1)^6,i=0..n);
%p A259322 [seq(f(n),n=0..40)];
%o A259322 (PARI) Vec(x*(x^6+722*x^5+10543*x^4+23548*x^3+10543*x^2+722*x+1)/(x-1)^8 + O(x^100)) \\ _Colin Barker_, Jun 29 2015
%o A259322 (PARI) a(n) = n*(192*n^6-336*n^4+196*n^2-31)/21 \\ _Charles R Greathouse IV_, Jun 29 2015
%Y A259322 Cf. A000447, A002309, A016758.
%K A259322 nonn,easy
%O A259322 1,2
%A A259322 _N. J. A. Sloane_, Jun 24 2015