A282549
Coefficients in q-expansion of E_2*E_4^3, where E_2 and E_4 are respectively the Eisenstein series A006352 and A004009.
Original entry on oeis.org
1, 696, 161928, 12599904, -22912728, -6132581424, -107015308128, -1012991092032, -6676225539480, -34225591158312, -145164618698832, -530958452207328, -1722320395791072, -5059903726594416, -13673185634909376, -34406198518205376, -81397333990275864
Offset: 0
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terms = 17;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E2[x]*E4[x]^3 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)
A282777
Expansion of phi_{16, 1}(x) where phi_{r, s}(x) = Sum_{n, m>0} m^r * n^s * x^{m*n}.
Original entry on oeis.org
0, 1, 65538, 43046724, 4295098372, 152587890630, 2821196197512, 33232930569608, 281483566907400, 1853020317992013, 10000305176108940, 45949729863572172, 184889914172333328, 665416609183179854, 2178019803670969104, 6568408813691796120
Offset: 0
- George E. Andrews and Bruce C. Berndt, Ramanujan's lost notebook, Part III, Springer, New York, 2012. See p. 212.
Cf.
A064987 (phi_{2, 1}),
A281372 (phi_{4, 1}),
A282050 (phi_{6, 1}),
A282060 (phi_{8, 1}),
A282254 (phi_{10, 1}),
A282548 (phi_{12, 1}),
A282597 (phi_{14, 1}), this sequence (phi_{16, 1}).
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Table[If[n==0, 0, n * DivisorSigma[15, n]], {n, 0, 15}] (* Indranil Ghosh, Mar 11 2017 *)
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for(n=0, 15, print1(if(n==0, 0, n * sigma(n, 15)), ", ")) \\ Indranil Ghosh, Mar 11 2017
Showing 1-2 of 2 results.
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