A341247 Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^8.
1, 0, 8, 8, 36, 64, 148, 296, 562, 1080, 1920, 3440, 5890, 9992, 16532, 26920, 43175, 68144, 106260, 163472, 248824, 374504, 558212, 824208, 1206409, 1751360, 2522692, 3607456, 5122848, 7227392, 10132948, 14123000, 19573393, 26981768, 37003700, 50499952, 68595956
Offset: 8
Keywords
Crossrefs
Programs
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Maple
g:= proc(n) option remember; `if`(n=0, 1, add(add([0, d, -d, d] [1+irem(d, 4)], d=numtheory[divisors](j))*g(n-j), j=1..n)/n) end: b:= proc(n, k) option remember; `if`(k<2, `if`(n=0, 1-k, g(n)), (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))) end: a:= n-> b(n, 8): seq(a(n), n=8..44); # Alois P. Heinz, Feb 07 2021 -
Mathematica
nmax = 44; CoefficientList[Series[(-1 + Product[1/(1 + (-x)^k), {k, 1, nmax}])^8, {x, 0, nmax}], x] // Drop[#, 8] &
Formula
G.f.: (-1 + Product_{k>=1} (1 + x^(2*k - 1)))^8.
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