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 A338403 #22 Aug 27 2025 11:43:15 %S A338403 1,2,3,5,23,14,14,131,233,84,42,664,2339,2367,594,132,3166,18520, %T A338403 36265,24714,4719,429,14545,127511,408311,527757,266219,40898 %N A338403 Regular triangle read by rows: T(n,k) is the number of (n,k)-Duck words, for n>=1 and 0<=k<=n-1. %C A338403 See link for the definition of Duck word. %H A338403 Ilani Axelrod-Freed, <a href="https://arxiv.org/abs/2010.11834">312-Avoiding Reduced Valid Hook Configurations and Duck Words</a>, arXiv:2010.11834 [math.CO], 2020. See Definition 5.1 p. 11. %H A338403 Dimana Miroslavova Pramatarova, <a href="https://www.cee.org/sites/default/files/rsi/Papers/pramatarovadimana_193982_5452885_Pramatarova_Dimana_AnaMaria_Final.pdf">Investigating the Periodicity of Weighted Catalan Numbers and Generalizing Them to Higher Dimensions</a>, MIT Res. Sci. Instit. (2025). See pp. 15, 17. %e A338403 Triangle begins: %e A338403 1; %e A338403 2, 3; %e A338403 5, 23, 14; %e A338403 14, 131, 233, 84; %e A338403 42, 664, 2339, 2367, 594; %e A338403 ... %Y A338403 Cf. A000108 (column 0), A005700 (diagonal), A005789 (row sums), A031970 (column 1). %K A338403 nonn,tabl,more,changed %O A338403 1,2 %A A338403 _Michel Marcus_, Oct 24 2020