A289345 - OEIS

%I #15 Mar 05 2018 09:32:38

%S 1,-294,-40572,-9456216,-3013531458,-1095736644072,-430427492908056,

%T -177966281438573376,-76323096421188881292,-33643171872410204427918,

%U -15150435131179232328586968,-6940567145625149028384495432

%N Coefficients in expansion of E_6^(7/12).

%F G.f.: Product_{n>=1} (1-q^n)^(7*A288851(n)/12).

%F a(n) ~ c * exp(2*Pi*n) / n^(19/12), where c = -7 * Gamma(1/12) * Gamma(1/4)^(22/3) / (1024 * 6^(1/12) * Pi^7) = -0.2836006135316422535659652380776952016594933981... - _Vaclav Kotesovec_, Jul 08 2017, updated Mar 05 2018

%t nmax = 20; CoefficientList[Series[(1 - 504*Sum[DivisorSigma[5,k]*x^k, {k, 1, nmax}])^(7/12), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 08 2017 *)

%Y E_6^(k/12): A109817 (k=1), A289325 (k=2), A289326 (k=3), A289327 (k=4), A289328 (k=5), A289293 (k=6), this sequence (k=7), A289346 (k=8), A289347 (k=9), A289348 (k=10), A289349 (k=11).

%Y Cf. A013973 (E_6), A288851.

%K sign

%O 0,2

%A _Seiichi Manyama_, Jul 03 2017