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 A023875 Expansion of Product_{k>=1} (1 - x^k)^(-k^6). 5
 1, 1, 65, 794, 6970, 69251, 689896, 6309849, 55654858, 483526120, 4104495070, 33968248260, 275366110929, 2192975727284, 17169583920204, 132264358228507, 1003715206329332, 7511468689508580, 55479733165442038, 404709688656248024, 2917717129031507178 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1771 (first 451 terms from Alois P. Heinz) G. Almkvist, Asymptotic formulas and generalized Dedekind sums, Exper. Math., 7 (No. 4, 1998), pp. 343-359. Vaclav Kotesovec, Graph - The asymptotic ratio for 10000 terms Vaclav Kotesovec, A method of finding the asymptotics of q-series based on the convolution of generating functions, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 21. FORMULA a(n) ~ exp(Pi * 2^(27/8) * n^(7/8) / (7*15^(1/8)) - 45*Zeta(7) / (8*Pi^6)) / (2^(29/16) * 15^(1/16) * n^(9/16)), where Zeta(7) = A013665 = 1.00834927738192... . - Vaclav Kotesovec, Feb 27 2015 G.f.: exp( Sum_{n>=1} sigma_7(n)*x^n/n ). - Seiichi Manyama, Mar 05 2017 a(n) = (1/n)*Sum_{k=1..n} sigma_7(k)*a(n-k). - Seiichi Manyama, Mar 05 2017 MAPLE with(numtheory): a:= proc(n) option remember; `if`(n=0, 1,       add(add(d*d^6, d=divisors(j)) *a(n-j), j=1..n)/n)     end: seq(a(n), n=0..25);  # Alois P. Heinz, Nov 02 2012 MATHEMATICA max = 20; Series[ Product[1/(1 - x^k)^k^6, {k, 1, max}], {x, 0, max}] // CoefficientList[#, x] & (* Jean-François Alcover, Mar 05 2013 *) PROG (PARI) m=30; x='x+O('x^m); Vec(prod(k=1, m, 1/(1-x^k)^k^6)) \\ G. C. Greubel, Oct 31 2018 (MAGMA) m:=30; R:=PowerSeriesRing(Rationals(), m); Coefficients(R! ( (&*[1/(1-x^k)^k^6: k in [1..m]]) )); // G. C. Greubel, Oct 3012018 CROSSREFS Column k=6 of A144048. Sequence in context: A196639 A008516 A000540 * A301550 A027463 A305264 Adjacent sequences:  A023872 A023873 A023874 * A023876 A023877 A023878 KEYWORD nonn AUTHOR EXTENSIONS Definition corrected by Franklin T. Adams-Watters and R. J. Mathar, Dec 04 2006 STATUS approved

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Last modified April 16 17:01 EDT 2021. Contains 343050 sequences. (Running on oeis4.)