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A341385 Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^3.

%I A341385 #11 Feb 20 2021 05:40:59
%S A341385 1,6,27,92,279,762,1952,4725,10968,24551,53346,112932,233755,474288,
%T A341385 945384,1854517,3585534,6841182,12895246,24035841,44337672,80999765,
%U A341385 146644746,263249169,468817933,828658233,1454315508,2535217624,4391290854,7560034419,12939963016
%N A341385 Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^3.
%H A341385 Alois P. Heinz, <a href="/A341385/b341385.txt">Table of n, a(n) for n = 3..10000</a>
%F A341385 a(n) ~ A027346(n). - _Vaclav Kotesovec_, Feb 20 2021
%p A341385 g:= proc(n) option remember; `if`(n=0, 1, add(g(n-j)*add(d^2/
%p A341385      `if`(d::odd, 1, 2), d=numtheory[divisors](j)), j=1..n)/n)
%p A341385     end:
%p A341385 b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, `if`(n=0, 0,
%p A341385       g(n)), (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
%p A341385     end:
%p A341385 a:= n-> b(n, 3):
%p A341385 seq(a(n), n=3..33);  # _Alois P. Heinz_, Feb 10 2021
%t A341385 nmax = 33; CoefficientList[Series[(-1 + Product[(1 + x^k)^k, {k, 1, nmax}])^3, {x, 0, nmax}], x] // Drop[#, 3] &
%Y A341385 Cf. A026007, A027346, A321948, A327381, A341384, A341386, A341387, A341388, A341390, A341391.
%K A341385 nonn
%O A341385 3,2
%A A341385 _Ilya Gutkovskiy_, Feb 10 2021