A049135 Revert transform of (-1 + 3x - 2x^2 + x^3)/(2x - 1).

1, 1, 2, 6, 22, 88, 368, 1585, 6984, 31348, 142868, 659434, 3076432, 14483556, 68723800, 328322903, 1577959294, 7624155960, 37011662868, 180436535308, 883016392536, 4336268255420, 21361517691248, 105535705919116

Offset

1,3

Links

Table of n, a(n) for n=1..24.

Index entries for reversions of series

Formula

Recurrence: 23*(n-2)*(n-1)*n*(72*n^2 - 384*n + 485)*a(n) = 72*(n-2)*(n-1)*(216*n^3 - 1476*n^2 + 3183*n - 2171)*a(n-1) - 24*(n-2)*(1944*n^4 - 18144*n^3 + 61731*n^2 - 90333*n + 47597)*a(n-2) + 24*(2592*n^5 - 33264*n^4 + 166788*n^3 - 406284*n^2 + 477074*n - 213371)*a(n-3) - 48*(n-3)*(3*n - 13)*(3*n - 11)*(72*n^2 - 240*n + 173)*a(n-4). - Vaclav Kotesovec, Jan 02 2021

a(n) ~ (2*sqrt(3) - 3)^(1/4) * 2^(n - 3/2) * 3^(n-1) / (sqrt(Pi) * n^(3/2) * (3 - sqrt(2)*3^(1/4))^(n - 1/2)). - Vaclav Kotesovec, Jan 02 2021

Mathematica

Rest[CoefficientList[InverseSeries[Series[x*(-1 + 3x - 2x^2 + x^3)/(2x - 1), {x, 0, 40}], x], x]] (* Vaclav Kotesovec, Jan 02 2021 *)

Crossrefs

Sequence in context: A165538 A165539 A109033 * A049127 A199481 A049137

Adjacent sequences: A049132 A049133 A049134 * A049136 A049137 A049138

Keyword

nonn

Author

Olivier Gérard

Status

approved