This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A008674 #49 Aug 18 2025 22:25:45
%S A008674 1,1,1,2,2,3,4,5,6,8,10,11,14,16,19,23,26,30,35,40,45,52,58,65,74,82,
%T A008674 91,102,113,124,138,151,165,182,198,216,236,256,277,301,325,350,379,
%U A008674 407,437,471,504,539,578,617,658,703,748,795,847,899,953,1012,1071,1133,1200,1267,1337,1413,1489,1568,1653
%N A008674 Expansion of 1/((1-x)*(1-x^3)*(1-x^5)*(1-x^7)*(1-x^9)).
%C A008674 Number of partitions of n into odd parts <= 9. - _Seiichi Manyama_, Jun 04 2017
%C A008674 Number of partitions (d1,d2,...,d5) of n such that 0 <= d1/1 <= d2/2 <= ... <= d5/5. - _Seiichi Manyama_, Jun 04 2017
%H A008674 Seiichi Manyama, <a href="/A008674/b008674.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Vincenzo Librandi)
%H A008674 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=244">Encyclopedia of Combinatorial Structures 244</a>
%H A008674 <a href="/index/Rec#order_25">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1,1,-1,1,-2,2,-2,1,-2,2,-1,2,-2,2,-1,1,-1,1,-1,0,-1,1).
%F A008674 a(n) = floor((n^4+50*n^3+855*n^2+6030*n+23800)/22680 - n*(n mod 3)/81). - _Hoang Xuan Thanh_, Aug 12 2025
%p A008674 seq(coeff(series(1/mul(1-x^(2*j+1), j=0..4), x, n+1), x, n), n = 0..70); # _G. C. Greubel_, Sep 08 2019
%t A008674 CoefficientList[Series[1/((1-x)(1-x^3)(1-x^5)(1-x^7)(1-x^9)), {x,0,70}], x] (* _Vincenzo Librandi_, Jun 22 2013 *)
%t A008674 LinearRecurrence[{1,0,1,-1,1,-1,1,-2,2,-2,1,-2,2,-1,2,-2,2,-1,1,-1,1,-1, 0,-1,1}, {1,1,1,2,2,3,4,5,6,8,10,11,14,16,19,23,26,30,35,40,45,52,58, 65,74}, 70] (* _Harvey P. Dale_, Aug 13 2016 *)
%o A008674 (PARI) my(x='x+O('x^70)); Vec(1/prod(j=0,4,1-x^(2*j+1)) ) \\ _G. C. Greubel_, Sep 08 2019
%o A008674 (Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/&*[1-x^(2*j+1): j in [0..4]] )); // _G. C. Greubel_, Sep 08 2019
%o A008674 (Sage)
%o A008674 def A008674_list(prec):
%o A008674 P.<x> = PowerSeriesRing(ZZ, prec)
%o A008674 return P( 1/prod(1-x^(2*j+1) for j in (0..4)) ).list()
%o A008674 A008674_list(70) # _G. C. Greubel_, Sep 08 2019
%o A008674 (PARI) a(n) = (n^4+50*n^3+855*n^2+6030*n - n*280*(n%3) +23800)\22680 \\ _Hoang Xuan Thanh_, Aug 12 2025
%Y A008674 Cf. A259094.
%K A008674 nonn,easy
%O A008674 0,4
%A A008674 _N. J. A. Sloane_
%E A008674 Typo in name fixed by _Vincenzo Librandi_, Jun 22 2013