A289567
Coefficients in expansion of 1/E_6^(1/2).
Original entry on oeis.org
1, 252, 103572, 46355904, 21754545876, 10493652271032, 5153897870227008, 2563741466120209536, 1287429765611338091988, 651251466581383330576956, 331360676706818772917367912, 169399388595923901462013678656
Offset: 0
E_6^(k/12):
A289570 (k=-18),
A000706 (k=-12), this sequence (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).
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nmax = 20; CoefficientList[Series[(1 - 504*Sum[DivisorSigma[5,k]*x^k, {k, 1, nmax}])^(-1/2), {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 *)
A289571
Coefficients in expansion of q * Product_{n>=1} (1 - q^n)^24/E_6^(3/2).
Original entry on oeis.org
1, 732, 483336, 299831152, 179912034330, 105705360893664, 61212394149183536, 35074084087016521152, 19935701871161896669257, 11259521840932766778870360, 6326766973556024191050129528, 3540038281600931271753859693440
Offset: 1
G.f.: q + 732*q^2 + 483336*q^3 + 299831152*q^4 + 179912034330*q^5 + ...
-
nmax = 20; CoefficientList[Series[Product[(1 - x^k)^24, {k, 1, nmax}] / (1 - 504*Sum[DivisorSigma[5,k]*x^k, {k, 1, nmax}])^(3/2), {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 09 2017 *)
Showing 1-3 of 3 results.