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 A306145 Expansion of (1/(1 - x)) * Sum_{k>=0} x^(2*k+1) / Product_{j=1..2*k+1} (1 - x^j). 2
 0, 1, 2, 4, 6, 10, 15, 23, 33, 49, 69, 98, 135, 187, 253, 343, 456, 607, 797, 1045, 1355, 1755, 2252, 2884, 3666, 4651, 5863, 7375, 9226, 11517, 14310, 17741, 21904, 26988, 33130, 40586, 49558, 60394, 73383, 88996, 107642, 129958, 156519, 188178, 225734, 270335, 323078, 385494 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Partial sums of A027193. LINKS Joerg Arndt, Matters Computational (The Fxtbook), section 16.4.1 "Unrestricted partitions and partitions into m parts", page 347. FORMULA a(n) = A000070(n) - A304620(n). a(n) ~ exp(Pi*sqrt(2*n/3)) / (2^(5/2)*Pi*sqrt(n)). - Vaclav Kotesovec, Aug 20 2018 MATHEMATICA nmax = 47; CoefficientList[Series[1/(1 - x) Sum[x^(2 k + 1)/Product[(1 - x^j), {j, 1, 2 k + 1}], {k, 0, nmax}], {x, 0, nmax}], x] nmax = 47; CoefficientList[Series[(1 - EllipticTheta[4, 0, x])/(2 (1 - x) QPochhammer[x]), {x, 0, nmax}], x] CROSSREFS Cf. A000070, A027193, A304620. Sequence in context: A035294 A073818 A239288 * A143184 A309173 A116084 Adjacent sequences:  A306142 A306143 A306144 * A306146 A306147 A306148 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Aug 19 2018 STATUS approved

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Last modified April 6 08:06 EDT 2020. Contains 333267 sequences. (Running on oeis4.)