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A334498
Number of intervals in Fang's Schroeder-Tamari poset.
0
2, 8, 46, 320, 2500, 21120, 188758, 1760256, 16969756, 168022016, 1700483916, 17527963648, 183499999368, 1946861076480, 20896083575142, 226570927865856, 2478789884919084, 27336509563600896, 303635676268456996, 3394385993908879360, 38168423356190965688, 431472747874361540608
OFFSET
1,1
COMMENTS
Fang (2020), Theorem 4.2, gives a generating function.
REFERENCES
Wenjie Fang, A partial order on Motzkin paths, Discrete Math., 343 (2020), #111802. See Section 4.
LINKS
Wenjie Fang, A partial order on Motzkin paths, arXiv preprint arXiv:1801.04809 [math.CO], 2018.
FORMULA
a(n) ~ sqrt(5/9 + 1/sqrt(3)) * (4*sqrt(45 + 26*sqrt(3))/3)^n / (sqrt(Pi)*n^(5/2)). - Vaclav Kotesovec, May 07 2020
MATHEMATICA
Rest[CoefficientList[Series[(-1 + w^4*x^2 + w*(1 + 2*x) - w^3*(3*x + 2*x^2)) / (w*x*(-1 + w^2*x)) /. w -> Root[-1 + #1 + 2*x*#1^2 - 2*x*#1^3 - x*(1 + x)*#1^4 + x^2*#1^5 &, 1], {x, 0, 30}], x]] (* Vaclav Kotesovec, May 07 2020 *)
CROSSREFS
Cf. A307787.
Sequence in context: A266507 A202081 A258315 * A006664 A276367 A326351
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 07 2020
EXTENSIONS
More terms from Vaclav Kotesovec, May 07 2020
STATUS
approved