A279892
Eisenstein series E_18(q) (alternate convention E_9(q)), multiplied by 43867.
Original entry on oeis.org
43867, -28728, -3765465144, -3709938631392, -493547047383096, -21917724609403728, -486272786232443616, -6683009405824511424, -64690198594597187640, -479102079577959825624, -2872821917728374840144, -14520482234727711482016, -63736746640768788267744
Offset: 0
- J.-P. Serre, Course in Arithmetic, Chap. VII, Section 4.
Cf.
A006352 (E_2),
A004009 (E_4),
A013973 (E_6),
A008410 (E_8),
A013974 (E_10),
A029828 (691*E_12),
A058550 (E_14),
A029829 (3617*E_16), this sequence (43867*E_18),
A029830 (174611*E_20),
A279893 (77683*E_22),
A029831 (236364091*E_24).
-
terms = 13;
E18[x_] = 43867 - 28728*Sum[k^17*x^k/(1 - x^k), {k, 1, terms}];
E18[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)
A282047
Coefficients in q-expansion of E_4^4*E_6, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.
Original entry on oeis.org
1, 456, -146232, -133082976, -32170154808, -3378441902544, -155862776255328, -3969266446940352, -65538944782146360, -777506848190979672, -7105808014591457232, -52584752452485047328, -326903300701760852832, -1755591608260377411216
Offset: 0
- G. E. Andrews and B. C. Berndt, Ramanujan's lost notebook, Part III, Springer, New York, 2012, See p. 208.
-
terms = 14;
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
E4[x]^4*E6[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)
A282048
Coefficients in q-expansion of E_4^5*E_6, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.
Original entry on oeis.org
1, 696, -34632, -167186976, -64422848328, -11387712944304, -1037073232984608, -48892286706157632, -1378097272692189000, -26188038166214133672, -364779879415169299632, -3952277018332870144608, -34798618196377082329632, -257403706082325167732976
Offset: 0
- G. E. Andrews and B. C. Berndt, Ramanujan's lost notebook, Part III, Springer, New York, 2012, See p. 208.
-
terms = 14;
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
E4[x]^5*E6[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)
A282382
Coefficients in q-expansion of E_4^6*E_6, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.
Original entry on oeis.org
1, 936, 134568, -173988576, -104617833048, -27210540914064, -3910401774129888, -322823174243838912, -15429983442476298840, -469709326015243815672, -9973673112569954220432, -158215072218253260221088, -1972939697011615168926432
Offset: 0
-
terms = 13;
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
E4[x]^6*E6[x] + 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 *)
-
for(n=0, 15, print1(if(n==0, 0, n * sigma(n, 15)), ", ")) \\ Indranil Ghosh, Mar 11 2017
Showing 1-5 of 5 results.
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