A293471 - OEIS

A293471

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

1, 2, 20, 248, 3472, 53152, 878144, 15577984, 296411392, 6054973952, 132994708480, 3144712222720, 80063883022336, 2192452931723264, 64427309553434624, 2025284853319303168, 67859418068644069376, 2414526405567056052224, 90909088845844899430400, 3610058425696043667030016

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..19.

Index entries for sequences related to factorial numbers

FORMULA

a(n) ~ sqrt(Pi) * 2^(n + 1/2) * n^(n + 3/2) / exp(n-1). - Vaclav Kotesovec, Sep 16 2021

MATHEMATICA

Table[SeriesCoefficient[1/(1 + ContinuedFractionK[-2 Floor[(k + 1)/2] x, 1, {k, 1, n}])^n, {x, 0, n}], {n, 0, 19}]

Table[SeriesCoefficient[Sum[(2 k)!! x^k, {k, 0, n}]^n, {x, 0, n}], {n, 0, 19}]

CROSSREFS