cp's OEIS Frontend

A294305 Sum of the tenth powers of the parts in the partitions of n into two distinct parts.

%I A294305 #16 Feb 12 2018 03:50:41
%S A294305 0,0,1025,59050,1108650,10815226,71340451,352767124,1427557524,
%T A294305 4904576300,14914341925,40791300350,102769130750,240345147350,
%U A294305 529882277575,1105458926376,2206044295976,4218551412024,7792505423049,13913571680850,24163571680850,40817515234450
%N A294305 Sum of the tenth powers of the parts in the partitions of n into two distinct parts.
%H A294305 Colin Barker, <a href="/A294305/b294305.txt">Table of n, a(n) for n = 1..1000</a>
%H A294305 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A294305 <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (1,11,-11,-55,55,165,-165,-330,330,462,-462,-462,462,330,-330,-165,165,55,-55,-11,11,1,-1).
%F A294305 a(n) = Sum_{i=1..floor((n-1)/2)} i^10 + (n-i)^10.
%F A294305 From _Colin Barker_, Nov 21 2017: (Start)
%F A294305 G.f.: x^3*(1025 + 58025*x + 1038325*x^2 + 9068301*x^3 + 49036000*x^4 + 177845712*x^5 + 466571800*x^6 + 905612928*x^7 + 1343112850*x^8 + 1525782114*x^9 + 1343112850*x^10 + 906468090*x^11 + 466571800*x^12 + 178253064*x^13 + 49036000*x^14 + 9115128*x^15 + 1038325*x^16 + 59037*x^17 + 1025*x^18 + x^19) / ((1 - x)^12*(1 + x)^11).
%F A294305 a(n) = a(n-1) + 11*a(n-2) - 11*a(n-3) - 55*a(n-4) + 55*a(n-5) + 165*a(n-6) - 165*a(n-7) - 330*a(n-8) + 330*a(n-9) + 462*a(n-10) - 462*a(n-11) - 462*a(n-12) + 462*a(n-13) + 330*a(n-14) - 330*a(n-15) - 165*a(n-16) + 165*a(n-17) + 55*a(n-18) - 55*a(n-19) - 11*a(n-20) + 11*a(n-21) + a(n-22) - a(n-23) for n>23.
%F A294305 (End)
%t A294305 Table[Sum[i^10 + (n - i)^10, {i, Floor[(n-1)/2]}], {n, 30}]
%o A294305 (PARI) a(n) = sum(i=1, (n-1)\2, i^10 + (n-i)^10); \\ _Michel Marcus_, Nov 05 2017
%o A294305 (PARI) concat(vector(2), Vec(x^3*(1025 + 58025*x + 1038325*x^2 + 9068301*x^3 + 49036000*x^4 + 177845712*x^5 + 466571800*x^6 + 905612928*x^7 + 1343112850*x^8 + 1525782114*x^9 + 1343112850*x^10 + 906468090*x^11 + 466571800*x^12 + 178253064*x^13 + 49036000*x^14 + 9115128*x^15 + 1038325*x^16 + 59037*x^17 + 1025*x^18 + x^19) / ((1 - x)^12*(1 + x)^11) + O(x^40))) \\ _Colin Barker_, Nov 21 2017
%Y A294305 Cf. A294286, A294287, A294288, A294300, A294301, A294302, A294303, A294304.
%K A294305 nonn,easy
%O A294305 1,3
%A A294305 _Wesley Ivan Hurt_, Oct 27 2017