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.

A133053 Squares of Motzkin numbers.

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%I A133053 #9 Apr 22 2024 17:45:47
%S A133053 1,1,4,16,81,441,2601,16129,104329,697225,4787344,33616804,240591121,
%T A133053 1750167225,12912685956,96454967184,728405920089,5554407254841,
%U A133053 42724289649924,331213938112656
%N A133053 Squares of Motzkin numbers.
%H A133053 G. C. Greubel, <a href="/A133053/b133053.txt">Table of n, a(n) for n = 0..1000</a>
%H A133053 Cyril Banderier, Markus Kuba, Stephan Wagner, and Michael Wallner, <a href="https://arxiv.org/abs/2311.17226">Composition schemes: q-enumerations and phase transitions</a>, arXiv:2311.17226 [math.CO], 2023. See p. 7.
%F A133053 a(n) = A001006(n)^2.
%t A133053 CoefficientList[Series[(1 - x - (1 - 2x - 3x^2)^(1/2))/(2x^2), {x, 0, 50}], x]^2 (* or *) Table[Hypergeometric2F1[(1-n)/2, -n/2, 2, 4], {n, 0, 50}]^2 (* _G. C. Greubel_, Oct 03 2017 *)
%Y A133053 Cf. A000290, A001248, A007598. Motzkin numbers: A001006.
%K A133053 nonn
%O A133053 0,3
%A A133053 _Omar E. Pol_, Oct 30 2007