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%I #7 Aug 20 2015 08:11:00
%S 1,0,1,0,1,1,0,1,1,1,0,1,2,1,1,0,1,4,2,1,1,0,1,8,5,2,1,1,0,1,16,14,5,
%T 2,1,1,0,1,32,41,15,5,2,1,1,0,1,64,122,51,15,5,2,1,1,0,1,128,365,187,
%U 52,15,5,2,1,1,0,1,256,1094,715,202,52,15,5,2,1,1
%N Triangle obtained by considering certain successive approximations to the Bell numbers.
%F Each row has e.g.f. given by a truncated exponential series in exp(x)-1. For example the e.g.f. = 1 + (exp(x)-1) + (1/2)(exp(x)-1)^2 gives the sequence 1, 1, 2, 4, 8, 16... . Alternatively, first differences of columns gives triangle of Stirling numbers of 2nd kind A008277.
%e Triangle starts:
%e 1;
%e 0, 1;
%e 0, 1, 1;
%e 0, 1, 1, 1;
%e 0, 1, 2, 1, 1;
%e 0, 1, 4, 2, 1, 1;
%e 0, 1, 8, 5, 2, 1, 1;
%e 0, 1, 16, 14, 5, 2, 1;
%e ...
%Y Cf. A000110.
%K easy,nonn,tabl
%O 0,13
%A _Paul Boddington_, Jul 20 2005
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