A049122 Revert transform of x*(1 + 2*x)/(1 + 3*x + x^2).

1, 1, 0, 0, 1, -1, -1, 5, -5, -9, 34, -26, -85, 255, -120, -820, 1995, -245, -7960, 15800, 4755, -77175, 123815, 105445, -743699, 936529, 1536534, -7094790, 6576505, 19436599, -66736489, 39201501, 228580275, -616062205, 134736984, 2566177896, -5546263549, -1161261075

Offset: 1

Author

Olivier Gérard

Keywords

• sign

Links

• Index entries for reversions of series

Programs

Mathematica

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

Formula

Recurrence: 2*n*a(n) = -3*(n-2)*a(n-1) - (8*n - 27)*a(n-2) + 5*(n-3)*a(n-3). - Vaclav Kotesovec, Jan 02 2021

G.f.: (1 - 3*x - sqrt(1 + 2*x + 5*x^2)) / (2*(x-2)). - Vaclav Kotesovec, Jan 04 2021

Extensions

NAME multiplied by x. - R. J. Mathar, Jul 23 2023