%I #10 Feb 20 2021 05:47:07

%S 1,6,21,59,144,321,669,1323,2511,4604,8202,14253,24241,40449,66363,

%T 107234,170910,269004,418566,644436,982536,1484482,2223942,3305484,

%U 4876620,7144455,10398123,15039564,21624678,30919323,43973708,62222844,87619212,122810585

%N Expansion of (-1 + Product_{k>=1} 1 / (1 - x^k))^3.

%H Alois P. Heinz, <a href="/A341221/b341221.txt">Table of n, a(n) for n = 3..10000</a>

%F a(n) ~ A000716(n). - _Vaclav Kotesovec_, Feb 20 2021

%p b:= proc(n, k) option remember; `if`(k<2, `if`(n=0, 1-k, combinat[

%p numbpart](n)), (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))

%p end:

%p a:= n-> b(n, 3):

%p seq(a(n), n=3..36); # _Alois P. Heinz_, Feb 07 2021

%t nmax = 36; CoefficientList[Series[(-1 + Product[1/(1 - x^k), {k, 1, nmax}])^3, {x, 0, nmax}], x] // Drop[#, 3] &

%Y Column k=3 of A060642.

%Y Cf. A000041, A000716, A048574, A327381, A341222, A341223, A341225, A341226, A341227, A341228.

%K nonn

%O 3,2

%A _Ilya Gutkovskiy_, Feb 07 2021