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%I #8 Jul 21 2018 07:23:48
%S 1,1,10,4159,162045118,1063421637466546,1858323116289048481112500,
%T 1253322341309506161980784960477550459,
%U 445827827888374514639499681047571455105640696771958,109534636154930845670316103395158313783593902542091687316468724140446
%N a(n) = [x^n] 1/(1 - x/(1 - 3^n*x/(1 - 5^n*x/(1 - 7^n*x/(1 - 9^n*x/(1 - ...)))))), a continued fraction.
%F a(n) = A291261(n,n).
%F a(n) ~ c * ((2*n-1)!!)^n ~ c * 2^(n^2 + n/2) * n^(n^2) / exp(n^2 + 1/24), where c = 1/QPochhammer(exp(-1)) = 1.9824409074128737036856824655613120156828827... - _Vaclav Kotesovec_, Aug 26 2017, updated Jul 21 2018
%t Table[SeriesCoefficient[1/(1 + ContinuedFractionK[-(2 i - 1)^n x, 1, {i, 1, n}]), {x, 0, n}], {n, 0, 9}]
%Y Main diagonal of A291261.
%Y Cf. A291547.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Aug 22 2017