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 A384253 #9 May 26 2025 05:48:59 %S A384253 2,1,2,1,9,1,181,1,8065,1,604801,1,68428801,1,10897286401,1, %T A384253 2324754432001,1,640237370572801,1,221172909834240001,1, %U A384253 93666727314800640001,1,47726800133326110720001,1,28806532937614688256000001,1,20325889640780924033433600001,1,16578303738261941164769280000001 %N A384253 a(n) = 1 + ((1+(-1)^(n-1))*(n-1)!)/(n+1). %H A384253 Ivan V. Morozov, <a href="https://arxiv.org/abs/2505.16201">On Quotients of a More General Theorem of Wilson</a>, arXiv:2505.16201 [math.NT], 2025. See Z formula (7) p. 2 and p. 9. %F A384253 a(2*n+1) = 1 + A060593(n), a(2n) = 1. %F A384253 D-finite with recurrence (n+1)*a(n) -(n-2)*(n-1)^2*a(n-2) +(n-3)*(n^2-n+1)=0. - _R. J. Mathar_, May 26 2025 %o A384253 (PARI) a(n) = 1 + ((1+(-1)^(n-1))*(n-1)!)/(n+1); %Y A384253 Cf. A060593. %K A384253 nonn %O A384253 1,1 %A A384253 _Michel Marcus_, May 23 2025