|
|
A185089
|
|
A transform of the little Schroeder numbers.
|
|
1
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
|
|
LINKS
|
|
|
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)
|
|
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 *)
|
|
PROG
|
(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
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|