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 A331329 #23 Jan 09 2024 11:03:32 %S A331329 1,9,145,2625,50049,982729,19665841,398796225,8166636545,168502295625, %T A331329 3497529199185,72949645000065,1527671538372225,32100078290806665, %U A331329 676451066002195825,14290577765009652865,302557549412667613185,6417968867896642617225,136371773642235542394385 %N A331329 a(n) = binomial(5*n, n)*hypergeom([-4*n, -n], [-5*n], -1). %C A331329 Special case of generalized Delannoy numbers (see cross-references): %C A331329 T(n, k) = binomial(k*n, n)*hypergeom([(1-k)*n, -n], [-k*n], -1). %H A331329 Seiichi Manyama, <a href="/A331329/b331329.txt">Table of n, a(n) for n = 0..747</a> %H A331329 Lin Yang, Yu-Yuan Zhang, and Sheng-Liang Yang, <a href="https://doi.org/10.1016/j.laa.2023.12.021">The halves of Delannoy matrix and Chung-Feller properties of the m-Schröder paths</a>, Linear Alg. Appl. (2024). %F A331329 a(n) ~ sqrt(5 + 21/sqrt(17)) * (349 + 85*sqrt(17))^n / (sqrt(Pi*n) * 2^(5*n + 2)). - _Vaclav Kotesovec_, Feb 13 2021 %t A331329 a[n_] := Binomial[5 n, n] Hypergeometric2F1[-4 n, -n, -5 n, -1]; %t A331329 Array[a, 19, 0] %Y A331329 Cf. A001850 (k=2), A026000 (k=3), A026001 (k=4), this sequence (k=5), A341491 (k=6). %Y A331329 Cf. A008288, A181675, A341476, A341477. %K A331329 nonn %O A331329 0,2 %A A331329 _Peter Luschny_, Jan 31 2020