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 A307057 Expansion of 1/(2 - Product_{k>=2} 1/(1 - x^k)). 1
 1, 0, 1, 1, 3, 4, 10, 15, 33, 55, 111, 195, 380, 684, 1306, 2389, 4507, 8313, 15591, 28881, 53991, 100257, 187086, 347860, 648512, 1206656, 2248399, 4185087, 7796011, 14514195, 27033073, 50334299, 93741325, 174552379, 325067573, 605316388, 1127249250, 2099115548, 3909023438, 7279285948 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Invert transform of A002865. LINKS FORMULA a(0) = 1; a(n) = Sum_{k=1..n} A002865(k)*a(n-k). a(n) ~ c / r^n, where r = 0.53700045638650021831634004949965496126950171484122... is the root of the equation 1 - r = 2*QPochhammer[r] and c = 0.2143395760756683581919851351414497181589685708674442097498294834747517926... MATHEMATICA nmax = 39; CoefficientList[Series[1/(2 - Product[1/(1 - x^k), {k, 2, nmax}]), {x, 0, nmax}], x] a[0] = 1; a[n_] := a[n] =  Sum[(PartitionsP[k] - PartitionsP[k - 1]) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 39}] CROSSREFS Cf. A002865, A055887, A304969. Sequence in context: A103080 A055720 A054184 * A188022 A007007 A037952 Adjacent sequences:  A307054 A307055 A307056 * A307058 A307059 A307060 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Mar 21 2019 STATUS approved

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Last modified February 17 12:14 EST 2020. Contains 331996 sequences. (Running on oeis4.)