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 A316231 Expansion of Product_{k>=1} 1/(1 + q(k)*x^k), where q(k) = number of partitions of k into distinct parts (A000009). 1
 1, -1, 0, -2, 1, -2, 3, -3, 6, -8, 14, -10, 28, -26, 41, -73, 90, -112, 155, -221, 288, -501, 560, -799, 1153, -1610, 1953, -3095, 4073, -5224, 7295, -9536, 13536, -18402, 24757, -32936, 48714, -60790, 82101, -113247, 153330, -201522, 275713, -367041, 492991 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Table of n, a(n) for n=0..44. Eric Weisstein's World of Mathematics, Partition Function Q Index entries for sequences related to partitions FORMULA G.f.: exp(Sum_{k>=1} Sum_{j>=1} (-1)^k*q(j)^k*x^(j*k)/k). MATHEMATICA nmax = 44; CoefficientList[Series[Product[1/(1 + PartitionsQ[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x] nmax = 44; CoefficientList[Series[Exp[Sum[Sum[(-1)^k PartitionsQ[j]^k x^(j k)/k, {j, 1, nmax}], {k, 1, nmax}]], {x, 0, nmax}], x] a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d (-PartitionsQ[d])^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 44}] CROSSREFS Cf. A000009, A089254, A270995, A279785, A304786, A316230. Sequence in context: A109266 A022876 A242692 * A014781 A214500 A066016 Adjacent sequences: A316228 A316229 A316230 * A316232 A316233 A316234 KEYWORD sign AUTHOR Ilya Gutkovskiy, Jun 27 2018 STATUS approved

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Last modified December 1 05:26 EST 2023. Contains 367468 sequences. (Running on oeis4.)