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

0,3

Links

Table of n, a(n) for 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

Mathematica

Table[SeriesCoefficient[1/(1 + ContinuedFractionK[-(2 i - 1)^n x, 1, {i, 1, n}]), {x, 0, n}], {n, 0, 9}]

Crossrefs

Main diagonal of A291261.

Cf. A291547.

Sequence in context: A024139 A320983 A316397 * A294747 A199354 A336831

Adjacent sequences: A291329 A291330 A291331 * A291333 A291334 A291335

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 22 2017

Status

approved