A282328 -id:A282328 - cp's OEIS frontend

A279893 Eisenstein series E_22(q) (alternate convention E_11(q)), multiplied by 77683.

77683, -552, -1157628456, -5774114968608, -2427722831757864, -263214111328125552, -12109202528761173024, -308317316973972772416, -5091303792066668003880, -60399282006368937251976, -552000263214112485753456, -4084937969230504375869024, -25394838301602325644596256, -136379620048544616772836528, -646588586243917921590531648

Offset: 0

Seiichi Manyama, Dec 22 2016

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J.-P. Serre, Course in Arithmetic, Chap. VII, Section 4.

Seiichi Manyama, Table of n, a(n) for n = 0..10000

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).

Cf. A282047 (E_4^4*E_6), A282328 (E_4*E_6^3).

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 *)

G.f.: 77683 - 552 * Sum_{i>=1} sigma_21(i)q^i where sigma_21(n) is A013969.

a(n) = 57183*A282047(n) + 20500*A282328(n). - Seiichi Manyama, Feb 12 2017

A282404 Coefficients in q-expansion of E_4*E_6^4, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.

Original entry on oeis.org

1, -1776, 975888, -66529344, -79516693488, 9511628122080, 2031621786790848, 134911299030780288, 4962883791154433040, 119289719378991436368, 2051366007318600561120, 26893975935849646148928, 281804567385216854182848

Offset: 0

Seiichi Manyama, Feb 14 2017

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Seiichi Manyama, Table of n, a(n) for n = 0..1000

Cf. A013974 (E_4*E_6 = E_10), A282287 (E_4*E_6^2), A282328 (E_4*E_6^3), this sequence (E_4*E_6^4).

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]*E6[x]^4 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)

cp's OEIS Frontend

A279893 Eisenstein series E_22(q) (alternate convention E_11(q)), multiplied by 77683.

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