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%I #42 Sep 08 2022 08:44:36
%S 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 91,102,113,124,138,151,165,182,198,216,236,256,277,301,325,350,379,
%U 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 Expansion of 1/((1-x)*(1-x^3)*(1-x^5)*(1-x^7)*(1-x^9)).
%C Number of partitions of n into odd parts <= 9. - _Seiichi Manyama_, Jun 04 2017
%C Number of partitions (d1,d2,...,d5) of n such that 0 <= d1/1 <= d2/2 <= ... <= d5/5. - _Seiichi Manyama_, Jun 04 2017
%H Seiichi Manyama, <a href="/A008674/b008674.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Vincenzo Librandi)
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=244">Encyclopedia of Combinatorial Structures 244</a>
%H <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).
%p 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 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 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 (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 (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 (Sage)
%o def A008674_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( 1/prod(1-x^(2*j+1) for j in (0..4)) ).list()
%o A008674_list(70) # _G. C. Greubel_, Sep 08 2019
%Y Cf. A259094.
%K nonn,easy
%O 0,4
%A _N. J. A. Sloane_
%E Typo in name fixed by _Vincenzo Librandi_, Jun 22 2013
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