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 A305082 G.f.: Sum_{k>=1} x^k/(1-x^k) * Product_{k>=1} (1+x^k). 7
 0, 1, 3, 5, 9, 13, 20, 28, 39, 54, 71, 94, 124, 159, 201, 258, 322, 401, 499, 613, 750, 918, 1110, 1340, 1617, 1935, 2308, 2752, 3261, 3854, 4554, 5350, 6273, 7348, 8572, 9983, 11612, 13460, 15578, 18007, 20761, 23894, 27473, 31511, 36090, 41296, 47152, 53767 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Convolution of A000005 and A000009. Apart from initial zero this is the convolution of A341062 and A036469. - Omar E. Pol, Feb 16 2021 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 FORMULA a(n) ~ 3^(1/4)*(2*gamma + log(12*n/Pi^2)) * exp(Pi*sqrt(n/3)) / (4*Pi*n^(1/4)), where gamma is the Euler-Mascheroni constant A001620. MATHEMATICA nmax = 50; CoefficientList[Series[Sum[x^k/(1-x^k), {k, 1, nmax}]*Product[1+x^k, {k, 1, nmax}], {x, 0, nmax}], x] nmax = 50; CoefficientList[Series[((Log[1-x] + QPolyGamma[0, 1, x]) * QPochhammer[-1, x]) / (2*Log[x]), {x, 0, nmax}], x] CROSSREFS Cf. A000005, A000009, A006128, A015723, A209423. Cf. A001227, A048272, A067588, A090867, A036469, A341062. Sequence in context: A033499 A267262 A106607 * A007042 A178415 A249424 Adjacent sequences: A305079 A305080 A305081 * A305083 A305084 A305085 KEYWORD nonn AUTHOR Vaclav Kotesovec, May 25 2018 STATUS approved

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Last modified June 18 20:38 EDT 2024. Contains 373487 sequences. (Running on oeis4.)