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A341387
Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^5.
10
1, 10, 65, 320, 1330, 4872, 16255, 50335, 146775, 407045, 1082000, 2773045, 6884650, 16620225, 39135280, 90113553, 203347645, 450516450, 981491380, 2105504205, 4452798556, 9293254605, 19158353285, 39044262235, 78719105560, 157112112293, 310599279105
OFFSET
5,2
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, 5):
seq(a(n), n=5..31); # Alois P. Heinz, Feb 10 2021
MATHEMATICA
nmax = 31; CoefficientList[Series[(-1 + Product[(1 + x^k)^k, {k, 1, nmax}])^5, {x, 0, nmax}], x] // Drop[#, 5] &
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 10 2021
STATUS
approved