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A294279
Sum of the tenth powers of the parts in the partitions of n into two parts.
1
0, 2, 1025, 61098, 1108650, 10933324, 71340451, 354864276, 1427557524, 4924107550, 14914341925, 40912232702, 102769130750, 240910097848, 529882277575, 1107606410024, 2206044295976, 4225524980826, 7792505423049, 13933571680850, 24163571680850, 40869390083652
OFFSET
1,2
FORMULA
a(n) = Sum_{i=1..floor(n/2)} i^10 + (n-i)^10.
From Robert Israel, Oct 27 2017: (Start)
a(2*k) = (6144*k^10-16863*k^9+14080*k^8-4224*k^6+1056*k^4-132*k^2+5)*k/33.
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.
G.f.: x^2*(x^20+1023*x^19+59039*x^18+1036299*x^17+9117154*x^16+48940320*x^15
+178348744*x^14+465661416*x^13+907378474*x^12+1340492142*x^11+1528402822*x^10
+1340492142*x^9+908233636*x^8+465661416*x^7+178756096*x^6+48940320*x^5
+9163981*x^4+1036299*x^3+60051*x^2+1023*x+2)/((x^2-1)^11*(x-1)). (End)
MAPLE
f:= proc(n)
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)
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)
fi end proc:
map(f, [$1..50]); # Robert Israel, Oct 27 2017
MATHEMATICA
Table[Sum[i^10 + (n - i)^10, {i, Floor[n/2]}], {n, 30}]
CROSSREFS
Sequence in context: A354534 A004897 A004802 * A196292 A182447 A218437
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Oct 26 2017
STATUS
approved