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%I
%S 1,1,2,4,8,19,53,160,512,1753,6431,25072,103022,444145,2004281,
%T 9447784,46407476,236950873,1254862955,6880495528,38999582018,
%U 228195894313,1376543144453,8550048509440,54619642413848,358490894378881,2415134218161767,16686051606437104
%N Number of partitions of an n-element set avoiding the pattern 12|3.
%H A. M. Goyt, <a href="http://arXiv.org/abs/math.CO/0603481">Avoidance of partitions of a 3-element set</a>, arXiv:math/0603481 [math.CO], 2006-2007
%F a(0)=1, a(1)=1, a(n) = 1 + a(n-1) + Sum_{k=1..n-2} binomial(n-2, k)*a(n-k-2).
%F The e.g.f. satisfies the differential equation y'' = y' + y(e^x-1) + e^x.
%K nonn
%O 0,3
%A _Ralf Stephan_, May 08 2007
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