A290049
Coefficients in expansion of 691*E_8*E_10*E_12.
Original entry on oeis.org
691, 214776, 10042488, -31595258016, -37453557900168, -14820419119618224, -2593285239712936608, -222297419357081232192, -10663770067272328258440, -324599563661107722245352, -6891830216922929182318512, -109326152051786546417315808
Offset: 0
-
terms = 12;
E8[x_] = 1 + 480*Sum[k^7*x^k/(1 - x^k), {k, 1, terms}];
E10[x_] = 1 - 264*Sum[k^9*x^k/(1 - x^k), {k, 1, terms}];
E12[x_] = 1 + (65520/691)*Sum[k^11*x^k/(1 - x^k), {k, 1, terms}];
691*E8[x]*E10[x]*E12[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)
A299955
Coefficients in expansion of E_4^(3/2).
Original entry on oeis.org
1, 360, 24840, -465120, 57417480, -6800282640, 930889890720, -139401582644160, 22250341370421000, -3723955494287559480, 646515765251485521840, -115559140273640812421280, 21150946022800731753255840, -3948247836773858791840263120
Offset: 0
E_4^(k/8):
A108091 (k=1),
A289307 (k=2),
A289308 (k=3),
A289292 (k=4),
A289309 (k=5),
A289318 (k=6),
A289319 (k=7),
A004009 (k=8), this sequence (k=12),
A008410 (k=16),
A008411 (k=24),
A282012 (k=32),
A282015 (k=40).
Original entry on oeis.org
0, 29354332817, 1292515672236611166229929, 56911411397043798759062515920346474052, 2505895144465774474827581824222076409739506505294889, 110338336739674093788639219775047689525384763850603917156033805525
Offset: 0
A105097
Expansion of Delta(tau)/E_4(tau)^2.
Original entry on oeis.org
1, -504, 180252, -56364992, 16415391870, -4574618335008, 1237162549543256, -327377686829760000, 85212608926827807477, -21894492009015306942480, 5567179862617316105012532, -1403483985988949037403977984
Offset: 1
-
{a(n)=if(n<1,0,polcoeff( x*eta(x+x*O(x^n))^24/sum(k=1,n,480*sigma(k,7)*x^k,1),n))} /* Michael Somos, Apr 07 2005 */
A282540
Eisenstein series E_32(q) (alternate convention E_16(q)), multiplied by 7709321041217.
Original entry on oeis.org
7709321041217, 32640, 70093866303360, 20160859654708062720, 150525431711563807489920, 151991844177246093750032640, 43295116458269350559666465280, 5149788469617367127914995164160, 323250903208723929093223124860800
Offset: 0
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),
A282182 (1723168255201*E_30), this sequence (7709321041217*E_32).
-
terms = 9;
E32[x_] = 7709321041217 + 32640*Sum[k^31*x^k/(1 - x^k), {k, 1, terms}];
E32[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)
Comments