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A341251 Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^9.

%I A341251 #7 Feb 07 2021 13:53:05
%S A341251 1,0,9,9,45,81,201,414,828,1650,3060,5697,10131,17829,30564,51543,
%T A341251 85482,139455,224527,356436,559341,867405,1331208,2022525,3044331,
%U A341251 4542174,6720705,9866794,14377941,20804994,29903823,42709860,60631011,85575855,120118500,167716548
%N A341251 Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^9.
%H A341251 Alois P. Heinz, <a href="/A341251/b341251.txt">Table of n, a(n) for n = 9..10000</a>
%F A341251 G.f.: (-1 + Product_{k>=1} (1 + x^(2*k - 1)))^9.
%p A341251 g:= proc(n) option remember; `if`(n=0, 1, add(add([0, d, -d, d]
%p A341251       [1+irem(d, 4)], d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
%p A341251     end:
%p A341251 b:= proc(n, k) option remember; `if`(k<2, `if`(n=0, 1-k, g(n)),
%p A341251       (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))
%p A341251     end:
%p A341251 a:= n-> b(n, 9):
%p A341251 seq(a(n), n=9..44);  # _Alois P. Heinz_, Feb 07 2021
%t A341251 nmax = 44; CoefficientList[Series[(-1 + Product[1/(1 + (-x)^k), {k, 1, nmax}])^9, {x, 0, nmax}], x] // Drop[#, 9] &
%Y A341251 Cf. A000700, A001487, A022604, A327387, A338463, A341228, A341241, A341243, A341244, A341245, A341246, A341247.
%K A341251 nonn
%O A341251 9,3
%A A341251 _Ilya Gutkovskiy_, Feb 07 2021