A279893
Eisenstein series E_22(q) (alternate convention E_11(q)), multiplied by 77683.
Original entry on oeis.org
77683, -552, -1157628456, -5774114968608, -2427722831757864, -263214111328125552, -12109202528761173024, -308317316973972772416, -5091303792066668003880, -60399282006368937251976, -552000263214112485753456, -4084937969230504375869024, -25394838301602325644596256, -136379620048544616772836528, -646588586243917921590531648
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),
A279892 (43867*E_18),
A029830 (174611*E_20), this sequence (77683*E_22),
A029831 (236364091*E_24).
-
terms = 15;
E22[x_] = 77683 - 552*Sum[k^21*x^k/(1 - x^k), {k, 1, terms}];
E22[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)
A282000
Coefficients in q-expansion of E_4^3*E_6, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.
Original entry on oeis.org
1, 216, -200232, -85500576, -11218984488, -499862636784, -11084671590048, -152346382155072, -1474691273530920, -10921720940625672, -65489246355989232, -331011680696545248, -1452954445366288032, -5665058572086302256, -19968589327695656256
Offset: 0
- G. E. Andrews and B. C. Berndt, Ramanujan's lost notebook, Part III, Springer, New York, 2012, See p. 208.
-
terms = 15;
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]^3*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 *)
Showing 1-4 of 4 results.