A289540 Coefficients in expansion of 1/E_6^(1/12).
1, 42, 12852, 4780104, 1974512526, 863778376440, 391960077239304, 182430901827757632, 86505196617272556900, 41607881477457256661154, 20239469012268054187498440, 9935363620927698868439915544, 4914082482014906612773260362232
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..367
Crossrefs
Programs
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Mathematica
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 *)
Formula
G.f.: Product_{n>=1} (1-q^n)^(-A288851(n)/12).
a(n) ~ c * exp(2*Pi*n) / n^(11/12), where c = 2^(5/12) * Gamma(3/4)^(4/3) / (3^(1/6) * Pi^(1/3) * Gamma(1/12)) = 0.08654217651555778130817946575840803466... - Vaclav Kotesovec, Jul 26 2017, updated Mar 05 2018
a(0) = 1, a(n) = (1/n)*Sum_{k=1..n} A299503(k)*a(n-k) for n > 0. - Seiichi Manyama, Feb 27 2018