A185089 A transform of the little Schroeder numbers.
1, 1, 2, 3, 7, 14, 35, 81, 208, 517, 1351, 3492, 9261, 24521, 65862, 177247, 481191, 1310338, 3589143, 9862257, 27215012, 75320969, 209147407, 582264200, 1625342649, 4547350865, 12750836298, 35824579355, 100843670951, 284361285238, 803170176715
Offset: 0
Links
- Fung Lam, Table of n, a(n) for n = 0..2000
Programs
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Mathematica
CoefficientList[Series[(1-x+x^2-Sqrt[1-2*x-5*x^2+6*x^3+x^4])/(4*x^2*(1-x)), {x,0,50}], x] (* G. C. Greubel, Jun 22 2017 *) -
PARI
x='x+O('x^50); Vec((1-x+x^2-sqrt(1-2*x-5*x^2+6*x^3+x^4))/(4*x^2*(1-x))) \\ G. C. Greubel, Jun 22 2017
Formula
G.f.: (1-x+x^2-sqrt(1-2x-5x^2+6x^3+x^4))/(4x^2(1-x)).
G.f.: 1/(1-x-x^2/(1-2x^2/(1-x-x^2/(1-2x^2/(1-x-x^2/(1-2x^2/(1-... (continued fraction).
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k)*A001003(k).
conjecture: (n+2)*a(n) -3*(n+1)*a(n-1) +3*(2-n)*a(n-2) +(11*n-20)*a(n-3) +(11-5*n)*a(n-4) +(4-n)*a(n-5) =0. - R. J. Mathar, Nov 16 2011 (Formula verified and used for computations. - Fung Lam, Feb 24 2014)
Comments