A282287
Coefficients in q-expansion of E_4*E_6^2, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.
Original entry on oeis.org
1, -768, -19008, 67329024, 4834170816, 137655866880, 2122110676224, 21418943158272, 158760815970240, 928988742914304, 4512155542392960, 18847838706545664, 69519052583699712, 230952254655327744, 701948326302761472, 1975789128222443520
Offset: 0
-
terms = 16;
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]*E6[x]^2 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)
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 *)
A282595
Coefficients in q-expansion of E_2^2*E_6, where E_2 and E_6 are respectively the Eisenstein series A006352 and A013973.
Original entry on oeis.org
1, -552, 7992, 460896, -3450504, -88161264, -728085024, -3775195968, -14894175240, -48567693576, -137214605232, -347495426784, -804758753568, -1733365307184, -3511286411328, -6753825302976, -12422812497672, -21971174382288, -37567247938344
Offset: 0
-
terms = 19;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
E2[x]^2*E6[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)
A282331
Coefficients in q-expansion of E_6^4, where E_6 is the Eisenstein series A013973.
Original entry on oeis.org
1, -2016, 1457568, -411997824, 16227967392, 6497071680960, 440015323483008, 15172068869975808, 327221898778968480, 4913597307075535008, 55440561879404210880, 496424806634688962688, 3672744471642078903168, 23148319448757751932096
Offset: 0
-
terms = 14;
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
E6[x]^4 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)
A282433
Coefficients in q-expansion of E_6^5, where E_6 is the Eisenstein series A013973.
Original entry on oeis.org
1, -2520, 2457000, -1113204960, 199879986600, 4992350445936, -3054519828108000, -316433406335739840, -15444821445342229080, -469944493113793897080, -9973874479528786860432, -158211337782226162119840, -1972932224893221543809760
Offset: 0
-
terms = 13;
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
E6[x]^5 + 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}).
-
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 1-6 of 6 results.
Comments