A134824 Generated by reverse of Schroeder II o.g.f.

0, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1

Offset: 0

Author

Wolfdieter Lang, Nov 13 2007

Keywords

• sign
• easy

Comments

The o.g.f. S(x) for A001003 (Schroeder II) satisfies 2*S^2(x) + (1+x)*S(x) + x = 0.

Using the Lagrange series for y=S(x) with y=0+x*(y/A(y)) leads to the formula for Schroeder II numbers involving the Narayana triangle A001263. See the Narayana comment by B. Cloitre under A001003 and a multiple differentiation formula given there.

Links

• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

If the initial 0 is omitted, we get A153881.

Formula

G.f.: x*(1-2*x)/(1-x).

a(0)=0,a(1)=1, a(n)=-1, n>=2.