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A341246 Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^7.

%I A341246 #6 Feb 07 2021 13:59:19
%S A341246 1,0,7,7,28,49,105,203,364,672,1141,1960,3220,5250,8359,13104,20272,
%T A341246 30877,46522,69195,101941,148604,214697,307475,436849,615965,862246,
%U A341246 1199009,1656642,2275231,3106824,4219502,5701066,7664923,10256771,13663574,18123924,23941190
%N A341246 Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^7.
%F A341246 G.f.: (-1 + Product_{k>=1} (1 + x^(2*k - 1)))^7.
%p A341246 g:= proc(n) option remember; `if`(n=0, 1, add(add([0, d, -d, d]
%p A341246       [1+irem(d, 4)], d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
%p A341246     end:
%p A341246 b:= proc(n, k) option remember; `if`(k<2, `if`(n=0, 1-k, g(n)),
%p A341246       (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))
%p A341246     end:
%p A341246 a:= n-> b(n, 7):
%p A341246 seq(a(n), n=7..44);  # _Alois P. Heinz_, Feb 07 2021
%t A341246 nmax = 44; CoefficientList[Series[(-1 + Product[1/(1 + (-x)^k), {k, 1, nmax}])^7, {x, 0, nmax}], x] // Drop[#, 7] &
%Y A341246 Cf. A000700, A001485, A022602, A327385, A338463, A341226, A341241, A341243, A341244, A341245, A341247, A341251.
%K A341246 nonn
%O A341246 7,3
%A A341246 _Ilya Gutkovskiy_, Feb 07 2021