A291332 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.
1, 1, 10, 4159, 162045118, 1063421637466546, 1858323116289048481112500, 1253322341309506161980784960477550459, 445827827888374514639499681047571455105640696771958, 109534636154930845670316103395158313783593902542091687316468724140446
Offset: 0
Keywords
Programs
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Mathematica
Table[SeriesCoefficient[1/(1 + ContinuedFractionK[-(2 i - 1)^n x, 1, {i, 1, n}]), {x, 0, n}], {n, 0, 9}]
Formula
a(n) = A291261(n,n).
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