%I #6 Feb 07 2021 13:59:19

%S 1,0,7,7,28,49,105,203,364,672,1141,1960,3220,5250,8359,13104,20272,

%T 30877,46522,69195,101941,148604,214697,307475,436849,615965,862246,

%U 1199009,1656642,2275231,3106824,4219502,5701066,7664923,10256771,13663574,18123924,23941190

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

%F G.f.: (-1 + Product_{k>=1} (1 + x^(2*k - 1)))^7.

%p g:= proc(n) option remember; `if`(n=0, 1, add(add([0, d, -d, d]

%p [1+irem(d, 4)], d=numtheory[divisors](j))*g(n-j), j=1..n)/n)

%p end:

%p b:= proc(n, k) option remember; `if`(k<2, `if`(n=0, 1-k, g(n)),

%p (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))

%p end:

%p a:= n-> b(n, 7):

%p seq(a(n), n=7..44); # _Alois P. Heinz_, Feb 07 2021

%t nmax = 44; CoefficientList[Series[(-1 + Product[1/(1 + (-x)^k), {k, 1, nmax}])^7, {x, 0, nmax}], x] // Drop[#, 7] &

%Y Cf. A000700, A001485, A022602, A327385, A338463, A341226, A341241, A341243, A341244, A341245, A341247, A341251.

%K nonn

%O 7,3

%A _Ilya Gutkovskiy_, Feb 07 2021