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A341244 Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^5.

%I A341244 #6 Feb 07 2021 13:56:24
%S A341244 1,0,5,5,15,25,45,80,125,210,321,500,745,1110,1620,2326,3315,4660,
%T A341244 6500,8955,12261,16640,22425,29990,39870,52701,69230,90460,117620,
%U A341244 152225,196066,251455,321195,408710,518060,654317,823690,1033535,1292690,1611970,2004462,2485605
%N A341244 Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^5.
%F A341244 G.f.: (-1 + Product_{k>=1} (1 + x^(2*k - 1)))^5.
%p A341244 g:= proc(n) option remember; `if`(n=0, 1, add(add([0, d, -d, d]
%p A341244       [1+irem(d, 4)], d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
%p A341244     end:
%p A341244 b:= proc(n, k) option remember; `if`(k<2, `if`(n=0, 1-k, g(n)),
%p A341244       (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))
%p A341244     end:
%p A341244 a:= n-> b(n, 5):
%p A341244 seq(a(n), n=5..46);  # _Alois P. Heinz_, Feb 07 2021
%t A341244 nmax = 46; CoefficientList[Series[(-1 + Product[1/(1 + (-x)^k), {k, 1, nmax}])^5, {x, 0, nmax}], x] // Drop[#, 5] &
%Y A341244 Cf. A000700, A001483, A022600, A327383, A338463, A341223, A341241, A341243, A341245, A341246, A341247, A341251.
%K A341244 nonn
%O A341244 5,3
%A A341244 _Ilya Gutkovskiy_, Feb 07 2021