A134824 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

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

Table of n, a(n) for n=0..84.

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

FORMULA

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

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

E.g.f.: 1 + 2*x - exp(x). - Elmo R. Oliveira, Dec 23 2025

MATHEMATICA

PadRight[{0, 1}, 100, -1] (* Paolo Xausa, Mar 03 2026 *)

CROSSREFS

If the initial 0 is omitted, we get A153881.

Cf. A001003, A001263, A057428.