Search: a126860 -id:a126860
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A126859
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Numerators of coefficients in quasimodular form F_3(q) of level 1 and weight 12.
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+10
3
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0, 0, 1, 20, 102, 2288, 3773, 14232, 133616, 119904, 584517, 1927900, 4013432, 2569296, 14394518, 8365192, 14426496, 23381600, 151885575, 58125708, 269849564, 395149888, 195967551, 828880856, 398774464, 544543680, 4586626939, 1018905048, 1396485648
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OFFSET
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0,4
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LINKS
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FORMULA
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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.).
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EXAMPLE
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F_3(q) = (1/12)*q^2 + (20/3)*q^3 + 102*q^4 + (2288/3)*q^5 + 3773*q^6 + 14232*q^7 + ...
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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A126861
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Coefficients in quasimodular form 12*F_3(q) of level 1 and weight 12.
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+10
3
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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
(list;
graph;
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history;
text;
internal format)
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OFFSET
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0,4
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LINKS
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FORMULA
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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.).
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EXAMPLE
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12*F_3(q) = q^2 + 80*q^3 + 1224*q^4 + 9152*q^5 + 45276*q^6 + 170784*q^7 + 534464*q^8 + ...
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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