A282433 -id:A282433 - cp's OEIS frontend

A282431 Coefficients in q-expansion of E_2^5, where E_2 is the Eisenstein series A006352.

1, -120, 5400, -104160, 511800, 6770736, -19504800, -452207040, -2959622280, -12932941080, -44497080432, -129918587040, -335811977760, -788655411600, -1714912983360, -3498061536576, -6761506680840, -12481939678320, -22138262633160, -37922739116640

Offset: 0

Seiichi Manyama, Feb 15 2017

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

Cf. this sequence (E_2^5), A282015 (E_4^5), A282433 (E_6^5).

Cf. A006352 (E_2), A281374 (E_2^2), A282018 (E_2^3), A282210 (E_2^4), this sequence (E_2^5).

terms = 20;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
E2[x]^5 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)

A282182 Eisenstein series E_30(q) (alternate convention E_15(q)), multiplied by 1723168255201.

Original entry on oeis.org

1723168255201, -171864, -92268782591832, -11795091175438423776, -49536425459206569762648, -32012164592742919922046864, -6332441368275869747902027488, -553385882817076320573218661312, -26594665913504249904864455466840

Offset: 0

Seiichi Manyama, Feb 16 2017

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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), A279893 (77683*E_22), A029831 (236364091*E_24), A282356 (657931*E_26), A282401 (3392780147*E_28), this sequence (1723168255201*E_30).

Cf. A282382 (E_4^6*E_6), A282461 (E_4^3*E_6^3), A282433 (E_6^5).

terms = 9;
E30[x_] = 1723168255201 - 171864*Sum[k^29*x^k/(1 - x^k), {k, 1, terms}];
E30[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)

a(n) = 815806500201*A282382(n) + 881340705000*A282461(n) + 26021050000*A282433(n).

cp's OEIS Frontend

A282431 Coefficients in q-expansion of E_2^5, where E_2 is the Eisenstein series A006352.

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