A049133 Revert transform of (x - 1)^2/(1 - x - x^3).

1, 1, 2, 4, 8, 14, 15, -31, -308, -1520, -6138, -22260, -74745, -234503, -684931, -1828743, -4249668, -7308296, -592722, 75389838, 487028178, 2286167634, 9278268220, 34247910114, 117081254935, 371845391419, 1086709633580, 2836930639816, 6075557104011

Offset

1,3

Links

Table of n, a(n) for n=1..29.

Index entries for reversions of series

Formula

Recurrence: 2*n*(2*n - 1)*(26*n^2 - 125*n + 156)*a(n) = 3*(182*n^4 - 1291*n^3 + 3244*n^2 - 3388*n + 1158)*a(n-1) - 3*(78*n^4 - 973*n^3 + 3964*n^2 - 6793*n + 4431)*a(n-2) - (n-3)*(1690*n^3 - 10179*n^2 + 19241*n - 12657)*a(n-3) - 31*(n-4)*(n-3)*(26*n^2 - 73*n + 57)*a(n-4). - Vaclav Kotesovec, Jan 02 2021

a(n+1) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (-1)^k * binomial(n+1,k) * binomial(2*n-2*k,n-3*k). - Seiichi Manyama, Sep 27 2023

Mathematica

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

Crossrefs

Cf. A049128.

Sequence in context: A368490 A076380 A370840 * A063033 A128309 A074202

Adjacent sequences: A049130 A049131 A049132 * A049134 A049135 A049136

Keyword

sign

Author

Olivier Gérard

Status

approved