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A134824
Generated by reverse of Schroeder II o.g.f.
2
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
0,1
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.
FORMULA
G.f.: x*(1-2*x)/(1-x).
a(0)=0,a(1)=1, a(n)=-1, n>=2.
CROSSREFS
If the initial 0 is omitted, we get A153881.
Sequence in context: A165574 A165581 A165586 * A165476 A165596 A226523
KEYWORD
sign,easy
AUTHOR
Wolfdieter Lang, Nov 13 2007
STATUS
approved