A291331 - OEIS

A291331

a(n) = [x^n] 1/(1 - 2^n*x/(1 - 4^n*x/(1 - 6^n*x/(1 - 8^n*x/(1 - 10^n*x/(1 - ...)))))), a continued fraction.

1, 2, 80, 152064, 31832735744, 1278532180456243200, 15158097871912903189326725120, 75553979800594222861911290918096439607296, 213679399657239557797941463213636090471439135194537263104

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..8.

FORMULA

a(n) = A291260(n,n).

a(n) ~ c * 2^(n^2) * (n!)^n ~ c * Pi^(n/2) * (2*n)^(n^2 + n/2) / exp(n^2 - 1/12), where c = 1/QPochhammer(exp(-1)) = 1.982440907412873703685682465561312... - Vaclav Kotesovec, Jun 08 2019

MATHEMATICA

Table[SeriesCoefficient[1/(1 + ContinuedFractionK[-(2 i)^n x, 1, {i, 1, n}]), {x, 0, n}], {n, 0, 8}]

CROSSREFS

Main diagonal of A291260.

Cf. A291333.

Sequence in context: A008563 A059487 A156932 * A369468 A293290 A056972

Adjacent sequences: A291328 A291329 A291330 * A291332 A291333 A291334

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Aug 22 2017

STATUS

approved