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a(n) = (1/2)*(Bell(n+2)-Bell(n+1)+Bell(n)).
1

%I #15 Sep 08 2022 08:45:11

%S 1,2,6,21,83,363,1733,8942,49484,291871,1825501,12054705,83734241,

%T 609851830,4644041462,36883843101,304846039251,2616765134351,

%U 23286746418237,214489200063218,2041785040262972,20060079966396887,203156789589084133,2118391734395139205

%N a(n) = (1/2)*(Bell(n+2)-Bell(n+1)+Bell(n)).

%H Vincenzo Librandi, <a href="/A087649/b087649.txt">Table of n, a(n) for n = 0..100</a>

%F 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 E.g.f.: exp(exp(x) - 1) * (exp(2*x) + 1) / 2. - _Ilya Gutkovskiy_, Aug 09 2021

%o (Magma) [(1/2)*(Bell(n+2)-Bell(n+1)+Bell(n)): n in [0..30]]; // _Vincenzo Librandi_, Nov 13 2011

%Y Cf. A000110, A035098, A059606.

%K nonn

%O 0,2

%A _Vladeta Jovovic_, Sep 23 2003