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 A371698 #22 Jul 06 2025 17:19:20
%S A371698 2,9,54,323,1848,10293,56738,312327,1723692,9549785,53121654,
%T A371698 296593547,1661423104,9333552509,52565738570,296696569871,
%U A371698 1677887732820,9505147063713,53928737011358,306393222740883,1742919983985192,9925790283119429,56584658970159474,322879453747840023
%N A371698 Number of partial order-preserving or -reversing transformations of a chain of length n.
%H A371698 V. H. Fernandes, G. M. S. Gomes, and M. M. Jesus, <a href="http://dx.doi.org/10.1081/AGB-200047446">Presentations for some monoids of partial transformations on a finite chain</a>, Communications in Algebra, 33 (2005), 587-604, 2005.
%F A371698 a(n) = 4*Sum_{k=0..n-1} binomial(n-1, k)*binomial(n+k, k) - (1 + n*(2 ^ n - 1)).
%F A371698 a(n) = 2*A002003(n) - (1 + n*(2^n - 1)).
%o A371698 (GAP) List([1..40], n -> 4 * Sum([0 .. n - 1], k -> Binomial(n - 1, k) * Binomial(n + k, k)) - (1 + n * (2 ^ n - 1)));
%o A371698 (PARI) a(n) = 4 * sum(k=0, n-1, binomial(n -1, k)*binomial(n + k, k)) - (1 + n * (2 ^ n - 1)); \\ _Michel Marcus_, Apr 03 2024
%Y A371698 Cf. A002003.
%K A371698 nonn
%O A371698 1,1
%A A371698 _James Mitchell_, Apr 03 2024