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A341391
Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^8.
10
1, 16, 152, 1072, 6204, 31024, 138544, 564824, 2135902, 7580944, 25485560, 81734696, 251514840, 746123304, 2142114356, 5971477112, 16208165181, 42936937488, 111240873128, 282363615336, 703303327288, 1721329848680, 4144792701532, 9829483710112
OFFSET
8,2
LINKS
MAPLE
g:= proc(n) option remember; `if`(n=0, 1, add(g(n-j)*add(d^2/
`if`(d::odd, 1, 2), d=numtheory[divisors](j)), j=1..n)/n)
end:
b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, `if`(n=0, 0,
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..31); # Alois P. Heinz, Feb 10 2021
MATHEMATICA
nmax = 31; CoefficientList[Series[(-1 + Product[(1 + x^k)^k, {k, 1, nmax}])^8, {x, 0, nmax}], x] // Drop[#, 8] &
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 10 2021
STATUS
approved