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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 A344180 A151847 Adjacent sequences: A300505 A300506 A300507 * A300509 A300510 A300511 KEYWORD sign AUTHOR Ilya Gutkovskiy, Mar 07 2018 STATUS approved

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Last modified December 10 18:13 EST 2023. Contains 367717 sequences. (Running on oeis4.)