login
A300508
Expansion of Product_{k>=1} (1 - x^k)^p(k), where p(k) = number of partitions of k (A000041).
4
1, -1, -2, -1, -1, 3, 3, 9, 9, 10, 8, -1, -21, -45, -77, -130, -163, -198, -179, -108, 101, 451, 1058, 1878, 2999, 4276, 5595, 6511, 6446, 4443, -838, -11069, -28373, -54652, -91948, -140370, -198501, -259706, -311997, -332003, -285486, -118600, 239086, 881998, 1918851, 3470261
OFFSET
0,3
COMMENTS
Convolution inverse of A001970.
LINKS
FORMULA
G.f.: Product_{k>=1} (1 - x^k)^A000041(k).
MAPLE
with(numtheory): with(combinat):
b:= proc(n) option remember; `if`(n=0, 1, add(add(d*
numbpart(d), d=divisors(j))*b(n-j), j=1..n)/n)
end:
a:= proc(n) option remember; `if`(n=0, 1,
-add(b(n-i)*a(i), i=0..n-1))
end:
seq(a(n), n=0..60); # Alois P. Heinz, Mar 07 2018
MATHEMATICA
nmax = 45; CoefficientList[Series[Product[(1 - x^k)^PartitionsP[k], {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Mar 07 2018
STATUS
approved