A289570
Coefficients in expansion of 1/E_6^(3/2).
Original entry on oeis.org
1, 756, 501228, 311671584, 187266950892, 110121960638088, 63808586297102304, 36578013578688141504, 20797655630223547290348, 11749541312124028845092052, 6603568491137827506152966712, 3695593478842608407829235523808
Offset: 0
E_6^(k/12): this sequence (k=-18),
A000706 (k=-12),
A289567 (k=-6),
A109817 (k=1),
A289325 (k=2),
A289326 (k=3),
A289327 (k=4),
A289328 (k=5),
A289293 (k=6),
A289345 (k=7),
A289346 (k=8),
A289347 (k=9),
A289348 (k=10),
A289349 (k=11).
-
nmax = 20; CoefficientList[Series[(1 - 504*Sum[DivisorSigma[5,k]*x^k, {k, 1, nmax}])^(-3/2), {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 09 2017 *)
A289540
Coefficients in expansion of 1/E_6^(1/12).
Original entry on oeis.org
1, 42, 12852, 4780104, 1974512526, 863778376440, 391960077239304, 182430901827757632, 86505196617272556900, 41607881477457256661154, 20239469012268054187498440, 9935363620927698868439915544, 4914082482014906612773260362232
Offset: 0
E_6^(k/12):
A289570 (k=-18),
A000706 (k=-12),
A289567 (k=-6), this sequence (k=-1),
A109817 (k=1),
A289325 (k=2),
A289326 (k=3),
A289327 (k=4),
A289328 (k=5),
A289293 (k=6),
A289345 (k=7),
A289346 (k=8),
A289347 (k=9),
A289348 (k=10),
A289349 (k=11).
-
nmax = 20; CoefficientList[Series[(1 - 504*Sum[DivisorSigma[5,k]*x^k, {k, 1, nmax}])^(-1/12), {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 26 2017 *)
A289557
Expansion of Hypergeometric function F(1/12, 7/12; 1; 1728*x) in powers of x.
Original entry on oeis.org
1, 84, 62244, 64318800, 76748408100, 99281740718160, 135254824771706640, 191023977418391557440, 277044462249611005649700, 410066847753461267769800400, 616822552390756438979333761680, 940037569843512813004504652800320
Offset: 0