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A256235 Sum of all the parts in the partitions of 5n into 5 parts.

%I A256235 #23 Jun 14 2016 14:20:17
%S A256235 0,5,70,450,1680,4800,11310,23590,44600,78615,130550,207075,315600,
%T A256235 465790,667940,935250,1281520,1723970,2280330,2972455,3822500,4857510,
%U A256235 6104560,7596325,9365400,11450750,13890760,16731225,20017060,23801315,28135800,33081495
%N A256235 Sum of all the parts in the partitions of 5n into 5 parts.
%H A256235 Colin Barker, <a href="/A256235/b256235.txt">Table of n, a(n) for n = 0..1000</a>
%H A256235 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,0,-4,-1,-1,4,4,-1,-1,-4,0,1,1,1,-1).
%F A256235 a(n) = 5*n*A256225(n).
%F A256235 G.f.: 5*x*(2*x^14 +19*x^13 +97*x^12 +277*x^11 +591*x^10 +955*x^9 +1267*x^8 +1355*x^7 +1217*x^6 +880*x^5 +520*x^4 +231*x^3 +75*x^2 +13*x +1) / ((x -1)^6*(x +1)^3*(x^2 +1)^2*(x^2 +x +1)^2).
%e A256235 For n=2 there are 7 partitions of 5*2 = 10, so a(2) = 7*10 = 70.
%t A256235 Plus @@ Total /@ IntegerPartitions[5 #, {5}] & /@ Range[0, 31] (* _Michael De Vlieger_, Mar 20 2015 *)
%t A256235 CoefficientList[Series[5 x (2 x^14 + 19 x^13 + 97 x^12 + 277 x^11 + 591 x^10 + 955 x^9 + 1267 x^8 + 1355 x^7 + 1217 x^6 + 880 x^5 + 520 x^4 + 231 x^3 + 75 x^2 + 13 x + 1) / ((x - 1)^6 (x + 1)^3 (x^2 + 1)^2 (x^2 + x + 1)^2), {x, 0, 40}], x] (* _Vincenzo Librandi_, Mar 20 2015 *)
%t A256235 LinearRecurrence[{1,1,1,0,-4,-1,-1,4,4,-1,-1,-4,0,1,1,1,-1},{0,5,70,450,1680,4800,11310,23590,44600,78615,130550,207075,315600,465790,667940,935250,1281520},40] (* _Harvey P. Dale_, Jun 14 2016 *)
%o A256235 (PARI) concat(0, Vec(5*x*(2*x^14 +19*x^13 +97*x^12 +277*x^11 +591*x^10 +955*x^9 +1267*x^8 +1355*x^7 +1217*x^6 +880*x^5 +520*x^4 +231*x^3 +75*x^2 +13*x +1) / ((x -1)^6*(x +1)^3*(x^2 +1)^2*(x^2 +x +1)^2) + O(x^100)))
%Y A256235 Cf. A235988, A238328, A256225, A256239.
%K A256235 nonn,easy
%O A256235 0,2
%A A256235 _Colin Barker_, Mar 20 2015