A284837 - OEIS

%I #4 Apr 03 2017 20:36:46

%S 1,2,3,4,5,6,7,9,10,11,12,13,14,15,16,19,20,21,22,23,24,25,26,30,31,

%T 32,34,35,36,37,38,43,44,45,47,48,49,50,51,57,58,59,61,62,63,64,65,72,

%U 73,74,76,77,78,81,82,90,91,92,94,95,96,99,100,110,111,112,114,115,116,119,120,131,132,133,135

%N Expansion of Sum_{i>=1} x^(i^3)/(1 - x^(i^3)) * Product_{j=1..i} 1/(1 - x^(j^3)).

%C Total number of largest parts in all partitions of n into cubes (A000578).

%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>

%F G.f.: Sum_{i>=1} x^(i^3)/(1 - x^(i^3)) * Product_{j=1..i} 1/(1 - x^(j^3)).

%e a(10) = 11 because we have [8, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] and 1 + 10 = 11.

%t nmax = 75; Rest[CoefficientList[Series[Sum[x^i^3/(1 - x^i^3) Product[1/(1 - x^j^3), {j, 1, i}], {i, 1, nmax}], {x, 0, nmax}], x]]

%Y Cf. A000578, A003108, A046746, A092311, A281613, A284831.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Apr 03 2017