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A289567
Coefficients in expansion of 1/E_6^(1/2).
7
1, 252, 103572, 46355904, 21754545876, 10493652271032, 5153897870227008, 2563741466120209536, 1287429765611338091988, 651251466581383330576956, 331360676706818772917367912, 169399388595923901462013678656
OFFSET
0,2
LINKS
FORMULA
G.f.: Product_{n>=1} (1-q^n)^(-A288851(n)/2).
a(n) ~ c * exp(2*Pi*n) / sqrt(n), where c = 2^(5/2) * Gamma(3/4)^8 / (3*Pi^(5/2)) = 0.5480868931611627439175185425300450785609564636925943866686455998197... - Vaclav Kotesovec, Jul 09 2017, updated Mar 03 2018
MATHEMATICA
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 *)
CROSSREFS
1/E_k^(1/2): A289565 (k=2), A289566 (k=4), this sequence (k=6), A001943 (k=8), A289568 (k=10), A289569 (k=14).
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).
Cf. A000706 (1/E_6), A288851, A289293 (E_6^(1/2)).
Sequence in context: A183507 A203385 A248165 * A179714 A109929 A351484
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 08 2017
STATUS
approved