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A341390
Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^7.
10
1, 14, 119, 756, 3969, 18102, 74102, 278161, 972447, 3202521, 10022705, 30013914, 86475340, 240787680, 650356936, 1709167922, 4381936874, 10984062425, 26971690900, 64986689201, 153866265007, 358443604177, 822523519244, 1861072144260, 4155817046514
OFFSET
7,2
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, 7):
seq(a(n), n=7..31); # Alois P. Heinz, Feb 10 2021
MATHEMATICA
nmax = 31; CoefficientList[Series[(-1 + Product[(1 + x^k)^k, {k, 1, nmax}])^7, {x, 0, nmax}], x] // Drop[#, 7] &
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 10 2021
STATUS
approved