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%I #10 Feb 11 2018 10:55:57
%S 0,2,1025,61098,1108650,10933324,71340451,354864276,1427557524,
%T 4924107550,14914341925,40912232702,102769130750,240910097848,
%U 529882277575,1107606410024,2206044295976,4225524980826,7792505423049,13933571680850,24163571680850,40869390083652
%N Sum of the tenth powers of the parts in the partitions of n into two parts.
%H Robert Israel, <a href="/A294279/b294279.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{i=1..floor(n/2)} i^10 + (n-i)^10.
%F From _Robert Israel_, Oct 27 2017: (Start)
%F a(2*k) = (6144*k^10-16863*k^9+14080*k^8-4224*k^6+1056*k^4-132*k^2+5)*k/33.
%F a(2*k+1) = (6144*k^10+16896*k^9+14080*k^8-4224*k^6+1056*k^4-132*k^2+5)*k/33.
%F G.f.: x^2*(x^20+1023*x^19+59039*x^18+1036299*x^17+9117154*x^16+48940320*x^15
%F +178348744*x^14+465661416*x^13+907378474*x^12+1340492142*x^11+1528402822*x^10
%F +1340492142*x^9+908233636*x^8+465661416*x^7+178756096*x^6+48940320*x^5
%F +9163981*x^4+1036299*x^3+60051*x^2+1023*x+2)/((x^2-1)^11*(x-1)). (End)
%p f:= proc(n)
%p if n::even then (1/66)*n*(6*n^10-(16863/512)*n^9+55*n^8-66*n^6+66*n^4-33*n^2+5)
%p else (1/66*(n-1))*n*(2*n-1)*(n^2-n-1)*(3*n^6-9*n^5+2*n^4+11*n^3+3*n^2-10*n-5)
%p fi end proc:
%p map(f, [$1..50]); # _Robert Israel_, Oct 27 2017
%t Table[Sum[i^10 + (n - i)^10, {i, Floor[n/2]}], {n, 30}]
%K nonn,easy
%O 1,2
%A _Wesley Ivan Hurt_, Oct 26 2017
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