A029831
Eisenstein series E_24(q) (alternate convention E_12(q)), multiplied by 236364091.
Original entry on oeis.org
236364091, 131040, 1099243323360, 12336522153621120, 9221121336284413920, 1562118530273437631040, 103486260766565509822080, 3586400651444203277717760, 77352372210526124884754400, 1161399411211600265764157280
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),
A279893 (77683*E_22), this sequence (236364091*E_24).
-
terms = 10;
E24[x_] = 236364091 + 131040*Sum[k^23*x^k/(1 - x^k), {k, 1, terms}];
E24[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)
-
a(n)=if(n<1,236364091*(n==0),131040*sigma(n,23))
A282403
Coefficients in q-expansion of E_4^4*E_6^2, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.
Original entry on oeis.org
1, -48, -392688, -67089216, 37279185936, 15066490704480, 2098369148842944, 134803101024250752, 4960096515113176080, 119289357755096403984, 2051412780505054295520, 26894040676649639982144, 281804014682888704101312
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]^4* E6[x]^2 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)
A010839
Expansion of Product_{k >= 1} (1-x^k)^48.
Original entry on oeis.org
1, -48, 1080, -15040, 143820, -985824, 4857920, -16295040, 28412910, 38671600, -424520544, 1268350272, -1211937160, -4306546080, 18293091840, -23522231424, -26299018683, 137218594320, -150999182320, -134713340160
Offset: 0
1 - 48*x + 1080*x^2 - 15040*x^3 + 143820*x^4 - 985824*x^5 + 4857920*x^6 - 16295040*x^7 + ...
- Morris Newman, A table of the coefficients of the powers of eta(tau), Nederl. Akad. Wetensch. Proc. Ser. A. 59 = Indag. Math. 18 (1956), 204-216.
A282541
Coefficients in q-expansion of E_4^5*E_6^2, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.
Original entry on oeis.org
1, 192, -402048, -161431296, 20329262976, 23865942948480, 5794392238723584, 671204645516954112, 41947216018774335360, 1615253348424607402944, 42337765240473386384640, 812656088633074046171904, 12060155362281020231526912
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]^5* E6[x]^2 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)
Showing 1-4 of 4 results.