cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A334498 Number of intervals in Fang's Schroeder-Tamari poset.

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%I A334498 #14 May 07 2020 19:32:10
%S A334498 2,8,46,320,2500,21120,188758,1760256,16969756,168022016,1700483916,
%T A334498 17527963648,183499999368,1946861076480,20896083575142,
%U A334498 226570927865856,2478789884919084,27336509563600896,303635676268456996,3394385993908879360,38168423356190965688,431472747874361540608
%N A334498 Number of intervals in Fang's Schroeder-Tamari poset.
%C A334498 Fang (2020), Theorem 4.2, gives a generating function.
%D A334498 Wenjie Fang, A partial order on Motzkin paths, Discrete Math., 343 (2020), #111802. See Section 4.
%H A334498 Wenjie Fang, <a href="http://arxiv.org/abs/1801.04809">A partial order on Motzkin paths</a>, arXiv preprint arXiv:1801.04809 [math.CO], 2018.
%F A334498 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
%t A334498 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 *)
%Y A334498 Cf. A307787.
%K A334498 nonn
%O A334498 1,1
%A A334498 _N. J. A. Sloane_, May 07 2020
%E A334498 More terms from _Vaclav Kotesovec_, May 07 2020