Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #38 Oct 30 2023 01:44:45
%S 0,1,2052,177156,4202512,48828150,363524112,1977326792,8606744640,
%T 31382654013,100195363800,285311670732,744500215872,1792160394206,
%U 4057474577184,8650199741400,17626613022976,34271896307922,64397206034676,116490258898580,205200886312800
%N Expansion of phi_{11, 2}(x) where phi_{r, s}(x) = Sum_{n, m>0} m^r * n^s * x^{m*n}.
%C Multiplicative because A013957 is. - _Andrew Howroyd_, Jul 23 2018
%H Seiichi Manyama, <a href="/A280021/b280021.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = n^2*A013957(n) for n > 0.
%F a(n) = (6*A282549(n) - 5*A282792(n) + 4*A282576(n) - 5*A058550(n))/1728.
%F Sum_{k=1..n} a(k) ~ zeta(10) * n^12 / 12. - _Amiram Eldar_, Sep 06 2023
%F From _Amiram Eldar_, Oct 30 2023: (Start)
%F Multiplicative with a(p^e) = p^(2*e) * (p^(9*e+9)-1)/(p^9-1).
%F Dirichlet g.f.: zeta(s-2)*zeta(s-11). (End)
%t Table[If[n>0, n^2 * DivisorSigma[9, n], 0], {n, 0, 20}] (* _Indranil Ghosh_, Mar 12 2017 *)
%o (PARI) for(n=0, 20, print1(if(n==0, 0, n^2 * sigma(n, 9)),", ")) \\ _Indranil Ghosh_, Mar 12 2017
%Y Cf. A282097 (phi_{3, 2}), A282099 (phi_{5, 2}), A282751 (phi_{7, 2}), A282753 (phi_{9, 2}), this sequence (phi_{11, 2}).
%Y Cf. A282549 (E_2*E_4^3), A282792 (E_2^2*E_4*E_6), A282576 (E_2*E_6^2), A058550 (E_4^2*E_6 = E_14).
%Y Cf. A013957 (sigma_9(n)), A282254 (n*sigma_9(n)), this sequence (n^2*sigma_9(n)).
%Y Cf. A013668 (zeta(10)).
%K nonn,easy,mult
%O 0,3
%A _Seiichi Manyama_, Feb 22 2017