login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A126861
Coefficients in quasimodular form 12*F_3(q) of level 1 and weight 12.
3
0, 0, 1, 80, 1224, 9152, 45276, 170784, 534464, 1438848, 3507102, 7711600, 16053728, 30831552, 57578072, 100382304, 173117952, 280579200, 455656725, 697508496, 1079398256, 1580599552, 2351610612, 3315523424, 4785293568, 6534524160, 9173253878, 12226860576
OFFSET
0,4
FORMULA
F_3(q) = (15*E(2)^4*E(4) - 6*E(2)^6 - 12*E(2)^2*E(4)^2 + 7*E(4)^3 + 4*E(2)^3*E(6) - 12*E(2)*E(4)*E(6) + 4*E(6)^2)/35831808, where E(k) is the normalized Eisenstein series of weight k (cf. A006352, etc.).
EXAMPLE
12*F_3(q) = q^2 + 80*q^3 + 1224*q^4 + 9152*q^5 + 45276*q^6 + 170784*q^7 + 534464*q^8 + ...
CROSSREFS
Cf. A280024 (E_2^4*E_4), A308285 (E_2^6), A282752 (E_2^2*E_4^2), A008411 (E_4^3), A282780 (E_2^3*E_6), A282102 (E_2*E_4*E_6), A280869 (E_6^2).
Sequence in context: A275701 A168364 A296353 * A038727 A204476 A151603
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 15 2007
STATUS
approved