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 A301554 Expansion of Product_{k>=1} ((1 + x^k)/(1 - x^k))^(sigma_0(k)). 20
 1, 2, 6, 14, 32, 66, 138, 266, 512, 948, 1730, 3074, 5408, 9306, 15854, 26594, 44150, 72378, 117620, 189074, 301516, 476518, 747514, 1163470, 1798920, 2762040, 4215194, 6393196, 9642596, 14462518, 21581386, 32040562, 47345342, 69635866, 101974722, 148692638 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Convolution of A006171 and A107742. LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 FORMULA G.f.: Product_{i>=1, j>=1} (1 + x^(i*j))/(1 - x^(i*j)). - Ilya Gutkovskiy, May 23 2018 Conjecture: log(a(n)) ~ Pi * sqrt(n*log(n)/2). - Vaclav Kotesovec, Sep 03 2018 MAPLE with(numtheory): seq(coeff(series(mul(((1+x^k)/(1-x^k))^sigma[0](k), k=1..n), x, n+1), x, n), n = 0 .. 35); # Muniru A Asiru, Oct 29 2018 MATHEMATICA nmax = 50; CoefficientList[Series[Product[((1+x^k)/(1-x^k))^DivisorSigma[0, k], {k, 1, nmax}], {x, 0, nmax}], x] PROG (PARI) m=50; x='x+O('x^m); Vec(prod(k=1, m, prod(j=1, m+2, (1+x^(j*k))/(1-x^(j*k)) ))) \\ G. C. Greubel, Oct 29 2018 (Magma) m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((&*[(&*[(1 + x^(j*k))/(1-x^(j*k)): j in [1..(m+2)]]): k in [1..(m+2)]]))); // G. C. Greubel, Oct 29 2018 CROSSREFS Cf. A000005, A006171, A107742, A320237. Sequence in context: A327049 A035592 A327050 * A217941 A346679 A232434 Adjacent sequences: A301551 A301552 A301553 * A301555 A301556 A301557 KEYWORD nonn AUTHOR Vaclav Kotesovec, Mar 23 2018 STATUS approved

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Last modified November 29 10:31 EST 2022. Contains 358424 sequences. (Running on oeis4.)