A282576
Coefficients in q-expansion of E_2*E_6^2, where E_2 and E_6 are respectively the Eisenstein series A006352 and A013973.
Original entry on oeis.org
1, -1032, 244872, 11293536, -12738264, -6174312624, -106952602464, -1012788556608, -6677393391000, -34223823782376, -145162615601232, -530968614112224, -1722312703896288, -5059890748287984, -13673195356609728, -34406230066992576, -81397361282611992
Offset: 0
-
terms = 17;
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]*E6[x]^2 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)
A282210
Coefficients in q-expansion of E_2^4, where E_2 is the Eisenstein series shown in A006352.
Original entry on oeis.org
1, -96, 3168, -34944, -107808, 1955520, 16829568, 76708608, 258593760, 715480608, 1729546560, 3771497088, 7581237888, 14296261056, 25520442624, 43590539520, 71582414304, 113752634688, 175604039136, 264097115520, 388619703360, 559658001408, 792716685696
Offset: 0
-
terms = 23;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
E2[x]^4 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 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 *)
A282596
Coefficients in q-expansion of E_2*E_4^2*E_6, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively.
Original entry on oeis.org
1, -48, -196128, -33542976, -678319104, 12136422240, 509314518144, 7469015889792, 68272650653760, 458377820557584, 2454769903187520, 11035857376010304, 43103740076823552, 149954656815201504, 473331019057949952, 1375248429330791040, 3719662610125117632
Offset: 0
-
terms = 17;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
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}];
E2[x]* E4[x]^2 *E6[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)
A282752
Coefficients in q-expansion of E_2^2*E_4^2, where E_2 and E_4 are respectively the Eisenstein series A006352 and A004009.
Original entry on oeis.org
1, 432, 39312, -1711296, -14159664, 317412000, 5783500224, 47251354752, 263098098000, 1138294453104, 4105673192160, 12882680040384, 36171259008192, 92764213434144, 220523509245312, 491705284878720, 1037366470830672, 2086141009345632, 4022101701933264
Offset: 0
-
terms = 19;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E2[x]^2*E4[x]^2 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)
A282431
Coefficients in q-expansion of E_2^5, where E_2 is the Eisenstein series A006352.
Original entry on oeis.org
1, -120, 5400, -104160, 511800, 6770736, -19504800, -452207040, -2959622280, -12932941080, -44497080432, -129918587040, -335811977760, -788655411600, -1714912983360, -3498061536576, -6761506680840, -12481939678320, -22138262633160, -37922739116640
Offset: 0
-
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 *)
A282547
Coefficients in q-expansion of E_2*E_4*E_6^2, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively.
Original entry on oeis.org
1, -792, -648, 67840416, 3219716376, 16790031216, -1536150710304, -39898324202688, -522122582192040, -4650999065751096, -31648313780323632, -175516685804469024, -827282698744164768, -3413275186936731984, -12598131165680789568, -42296014044574387776
Offset: 0
-
terms = 16;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
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}];
E2[x]*E4[x]*E6[x]^2 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)
A282586
Coefficients in q-expansion of E_2^3*E_4, where E_2 and E_4 are respectively the Eisenstein series A006352 and A004009.
Original entry on oeis.org
1, 168, -13608, 210336, 1805496, -22562064, -322437024, -2063087808, -9165872520, -32250917496, -96383477232, -254377990944, -608736541728, -1346209592784, -2786771573568, -5459635814976, -10197462567432, -18283324047408, -31620880746504
Offset: 0
Cf.
A282019 (E_2*E_4),
A282208 (E_2^2*E_4), this sequence (E_2^3*E_4).
-
terms = 19;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E2[x]^3*E4[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)
A282780
Coefficients in q-expansion of E_2^3*E_6, where E_2 and E_6 are respectively the Eisenstein series A006352 and A013973.
Original entry on oeis.org
1, -576, 21168, 308736, -15034608, -39208320, 1590712128, 20299281408, 137107250640, 665776675008, 2599125524640, 8637331788288, 25350641846208, 67336913702016, 164742803455104, 376186503674880, 809848148403024, 1657081821679488, 3243133560510576
Offset: 0
Cf.
A282096 (E_2*E_6),
A282595 (E_2^2*E_6), this sequence (E_2^3*E_6).
-
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]^3*E6[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)
A282792
Coefficients in q-expansion of E_2^2*E_4*E_6, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively.
Original entry on oeis.org
1, -312, -122328, 1193376, 120735336, 123318576, -26119268064, -383848045248, -3132125965080, -18290795499096, -84925855577232, -331983655889184, -1133781877844448, -3470165144567184, -9697162366507968, -25093220330304576, -60786860467926552
Offset: 0
Cf.
A282102 (E_2*E_4*E_6), this sequence (E_2^2*E_4*E_6),
A282596 (E_2*E_4^2*E_6),
A282547 (E_2*E_4*E_6^2).
-
terms = 17;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
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]^2*E6[x]*E6[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)