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A341253 Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^10.

%I A341253 #5 Feb 07 2021 13:15:24
%S A341253 1,0,10,10,55,100,265,560,1175,2420,4667,9000,16575,30180,53470,93152,
%T A341253 159395,268190,444910,727360,1174563,1873320,2955010,4611960,7127305,
%U A341253 10912244,16560430,24924550,37217620,55160650,81174270,118651560,172316445,248718830,356892660
%N A341253 Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^10.
%F A341253 G.f.: (-1 + Product_{k>=1} (1 + x^(2*k - 1)))^10.
%p A341253 g:= proc(n) option remember; `if`(n=0, 1, add(add([0, d, -d, d]
%p A341253       [1+irem(d, 4)], d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
%p A341253     end:
%p A341253 b:= proc(n, k) option remember; `if`(k<2, `if`(n=0, 1-k, g(n)),
%p A341253       (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))
%p A341253     end:
%p A341253 a:= n-> b(n, 10):
%p A341253 seq(a(n), n=10..44);  # _Alois P. Heinz_, Feb 07 2021
%t A341253 nmax = 44; CoefficientList[Series[(-1 + Product[1/(1 + (-x)^k), {k, 1, nmax}])^10, {x, 0, nmax}], x] // Drop[#, 10] &
%Y A341253 Cf. A000700, A001488, A022605, A327388, A338463, A341236, A341241, A341243, A341244, A341245, A341246, A341247, A341251.
%K A341253 nonn
%O A341253 10,3
%A A341253 _Ilya Gutkovskiy_, Feb 07 2021