A305535 - OEIS

A305535

Expansion of 1/(1 - x/(1 - 2*x/(1 - 2*x/(1 - 4*x/(1 - 4*x/(1 - 6*x/(1 - 6*x/(1 - ...)))))))), a continued fraction.

1, 1, 3, 13, 75, 557, 5179, 58589, 784715, 12154061, 213593563, 4195613373, 91031201643, 2160916171181, 55687501548539, 1547866851663261, 46150908197995403, 1469089501918434957, 49722765216242122267, 1782934051704982201469, 67514992620138056010667

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OFFSET

0,3

COMMENTS

Invert transform of A000165, shifted right one place.

LINKS

Table of n, a(n) for n=0..20.

N. J. A. Sloane, Transforms

Index entries for sequences related to factorial numbers

FORMULA

a(n) ~ 2^(n-1) * (n-1)!. - Vaclav Kotesovec, Sep 18 2021

MATHEMATICA

nmax = 20; CoefficientList[Series[1/(1 - x/(1 + ContinuedFractionK[-2 Floor[(k + 1)/2] x, 1, {k, 1, nmax}])), {x, 0, nmax}], x]

nmax = 20; CoefficientList[Series[1/(1 - Sum[2^(k - 1) (k - 1)! x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

a[0] = 1; a[n_] := a[n] = Sum[2^(k - 1) (k - 1)! a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]

CROSSREFS

Cf. A000165, A051295, A051296, A112934, A141307, A292778.

Sequence in context: A034172 A000670 A032036 * A300793 A222427 A026072

Adjacent sequences: A305532 A305533 A305534 * A305536 A305537 A305538

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jun 04 2018

STATUS

approved