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.
%I A337351 #21 Feb 28 2025 06:20:53
%S A337351 1,10,110,1805,34770,731760,16295600,377438250,8999246900,
%T A337351 219399101415,5444124108810,137040309706725,3490834454580950,
%U A337351 89816746611096280,2330761164942308080,60932036847971297230,1603218808449019802550,42423276620326253035205
%N A337351 a(n) is the number of lattice paths from (0,0) to (3n,2n) using only the steps (1,0) and (0,1) and which do not touch any other points of the form (3k,2k).
%C A337351 The terms of this sequence may be computed via a determinant; see Lemma 10.7.2 of the Krattenthaler reference for details.
%H A337351 Christian Krattenthaler, <a href="https://www.mat.univie.ac.at/~kratt/artikel/encylatt.pdf">"Lattice path enumeration"</a>. In: Handbook of Enumerative Combinatorics. Edited by Miklos Bona. CRC Press, 2015, pages 589-678.
%H A337351 R. J. Mathar, <a href="https://vixra.org/abs/2502.0097">The Eggenberger-Polya urn process: Probabilities of revisited ball ratios</a>, vixra:2502.0097 (2025) Table 4
%F A337351 G.f.: 2 - 1 / (Sum_{n>=0} binomial(5*n,2*n) * x^n).
%o A337351 (PARI) seq(n)={Vec(2 - 1/(O(x*x^n) + sum(k=0, n, binomial(5*k,2*k)*x^k)))} \\ _Andrew Howroyd_, Aug 25 2020
%Y A337351 Cf. A337291, A337292, A337350, A337352.
%K A337351 nonn,easy
%O A337351 0,2
%A A337351 _Lucas A. Brown_, Aug 24 2020