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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Convolution inverse of A001970.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..3000

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

Cf. A000041, A001970, A261049.

Sequence in context: A216655 A242884 A197219 * A120013 A151847 A179743

Adjacent sequences:  A300505 A300506 A300507 * A300509 A300510 A300511

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Mar 07 2018

STATUS

approved

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Last modified August 7 14:43 EDT 2020. Contains 336276 sequences. (Running on oeis4.)