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A282753
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Expansion of phi_{9, 2}(x) where phi_{r, s}(x) = Sum_{n, m>0} m^r * n^s * x^{m*n}.
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3
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0, 1, 516, 19692, 264208, 1953150, 10161072, 40353656, 135274560, 387597717, 1007825400, 2357947812, 5202783936, 10604499542, 20822486496, 38461429800, 69260574976, 118587876786, 200000421972, 322687698140, 516037855200, 794644193952, 1216701070992
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ zeta(8) * n^10 / 10. - Amiram Eldar, Sep 06 2023
Multiplicative with a(p^e) = p^(2*e) * (p^(7*e+7)-1)/(p^7-1).
Dirichlet g.f.: zeta(s-2)*zeta(s-9). (End)
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MATHEMATICA
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Table[If[n>0, n^2 * DivisorSigma[7, n], 0], {n, 0, 22}] (* Indranil Ghosh, Mar 12 2017 *)
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PROG
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(PARI) for(n=0, 22, print1(if(n==0, 0, n^2 * sigma(n, 7)), ", ")) \\ Indranil Ghosh, Mar 12 2017
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CROSSREFS
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Cf. A013955 (sigma_7(n)), A282060 (n*sigma_7(n)), this sequence (n^2*sigma_7(n)).
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KEYWORD
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nonn,easy,mult
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AUTHOR
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STATUS
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approved
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