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 A087649 #18 Nov 27 2024 11:40:10 %S A087649 1,2,6,21,83,363,1733,8942,49484,291871,1825501,12054705,83734241, %T A087649 609851830,4644041462,36883843101,304846039251,2616765134351, %U A087649 23286746418237,214489200063218,2041785040262972,20060079966396887,203156789589084133,2118391734395139205 %N A087649 a(n) = (1/2)*(Bell(n+2)-Bell(n+1)+Bell(n)). %H A087649 Vincenzo Librandi, <a href="/A087649/b087649.txt">Table of n, a(n) for n = 0..100</a> %H A087649 Reinis Cirpons, James East, and James D. Mitchell, <a href="https://arxiv.org/abs/2411.14693">Transformation representations of diagram monoids</a>, arXiv:2411.14693 [math.RA], 2024. See pp. 3, 33. %F A087649 G.f.: (1-x+x^2)/(2*x*Q(0)) - 1/(2*x) + 1/2, where Q(k)= 1 - x - x/(1 - x*(2*k+1)/(1 - x - x/(1 - x*(2*k+2)/Q(k+1)))); (continued fraction). - _Sergei N. Gladkovskii_, May 13 2013 %F A087649 E.g.f.: exp(exp(x) - 1) * (exp(2*x) + 1) / 2. - _Ilya Gutkovskiy_, Aug 09 2021 %o A087649 (Magma) [(1/2)*(Bell(n+2)-Bell(n+1)+Bell(n)): n in [0..30]]; // _Vincenzo Librandi_, Nov 13 2011 %Y A087649 Cf. A000110, A035098, A059606. %K A087649 nonn %O A087649 0,2 %A A087649 _Vladeta Jovovic_, Sep 23 2003