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A341246
Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^7.
9
1, 0, 7, 7, 28, 49, 105, 203, 364, 672, 1141, 1960, 3220, 5250, 8359, 13104, 20272, 30877, 46522, 69195, 101941, 148604, 214697, 307475, 436849, 615965, 862246, 1199009, 1656642, 2275231, 3106824, 4219502, 5701066, 7664923, 10256771, 13663574, 18123924, 23941190
OFFSET
7,3
FORMULA
G.f.: (-1 + Product_{k>=1} (1 + x^(2*k - 1)))^7.
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, 7):
seq(a(n), n=7..44); # Alois P. Heinz, Feb 07 2021
MATHEMATICA
nmax = 44; CoefficientList[Series[(-1 + Product[1/(1 + (-x)^k), {k, 1, nmax}])^7, {x, 0, nmax}], x] // Drop[#, 7] &
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 07 2021
STATUS
approved