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A341393 Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^9.

%I A341393 #8 Feb 10 2021 19:00:55
%S A341393 1,18,189,1464,9252,50292,243117,1068939,4344660,16522967,59349627,
%T A341393 202844007,663615180,2088375867,6347592999,18698498610,53538715836,
%U A341393 149375490453,406987481852,1084906793142,2834211905622,7266665613438,18308976116535
%N A341393 Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^9.
%H A341393 Alois P. Heinz, <a href="/A341393/b341393.txt">Table of n, a(n) for n = 9..10000</a>
%p A341393 g:= proc(n) option remember; `if`(n=0, 1, add(g(n-j)*add(d^2/
%p A341393      `if`(d::odd, 1, 2), d=numtheory[divisors](j)), j=1..n)/n)
%p A341393     end:
%p A341393 b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, `if`(n=0, 0,
%p A341393       g(n)), (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
%p A341393     end:
%p A341393 a:= n-> b(n, 9):
%p A341393 seq(a(n), n=9..31);  # _Alois P. Heinz_, Feb 10 2021
%t A341393 nmax = 31; CoefficientList[Series[(-1 + Product[(1 + x^k)^k, {k, 1, nmax}])^9, {x, 0, nmax}], x] // Drop[#, 9] &
%Y A341393 Cf. A026007, A321954, A327387, A341384, A341385, A341386, A341387, A341388, A341390, A341391, A341394.
%K A341393 nonn
%O A341393 9,2
%A A341393 _Ilya Gutkovskiy_, Feb 10 2021