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A304966
Expansion of Product_{k>=1} 1/(1 - x^k)^(p(k)-1), where p(k) = number of partitions of k (A000041).
9
1, 0, 1, 2, 5, 8, 18, 30, 61, 107, 203, 358, 663, 1162, 2093, 3666, 6481, 11258, 19652, 33874, 58464, 100046, 171032, 290563, 492745, 831393, 1399655, 2346707, 3924873, 6541472, 10875575, 18025629, 29804125, 49143254, 80841455, 132651457, 217179366, 354745107, 578215807
OFFSET
0,4
COMMENTS
Euler transform of A000065.
Convolution of the sequences A001970 and A010815.
FORMULA
G.f.: Product_{k>=1} 1/(1 - x^k)^A000065(k).
MAPLE
with(combinat): with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
numbpart(d)-d, d=divisors(j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..40); # Alois P. Heinz, May 22 2018
MATHEMATICA
nmax = 38; CoefficientList[Series[Product[1/(1 - x^k)^(PartitionsP[k] - 1), {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d (PartitionsP[d] - 1), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 38}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 22 2018
STATUS
approved