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%I #10 Feb 14 2022 01:25:06
%S 1,1,1,2,2,1,5,4,3,1,15,9,7,4,1,52,24,16,11,5,1,203,76,40,27,16,6,1,
%T 877,279,116,67,43,22,7,1,4140,1156,395,183,110,65,29,8,1,21147,5296,
%U 1551,578,293,175,94,37,9,1,115975,26443,6847,2129,871,468,269,131,46,10,1
%N Triangle read by rows: T(n,0)=B(n) (the Bell numbers, A000110(n)), T(n,k)=0 for k < 0 or k > n, T(n,k) = T(n-1,k) + T(n-1,k-1) for n >= 1, 0 <= k <= n.
%C Row sums = 1, 2, 5, 13, 36, 109, 369, ...
%C Columns 0,1 and 2 yield A000110, A005001 and A029761, respectively.
%e First few rows of the triangle:
%e 1;
%e 1, 1;
%e 2, 2, 1;
%e 5, 4, 3, 1;
%e 15, 9, 7, 4, 1;
%e 52, 24, 16, 11, 5, 1;
%e 203, 76, 40, 27, 16, 6, 1;
%e ...
%e (4,3) = 16 = 7 + 9 = (3,3) + (3,2).
%p with(combinat): T:=proc(n,k) if k=0 then bell(n) elif k<0 or k>n then 0 else T(n-1,k)+T(n-1,k-1) fi end: for n from 0 to 11 do seq(T(n,k),k=0..n) od; # yields sequence in triangular form
%Y Cf. A000110, A005001, A029761.
%K nonn,tabl
%O 0,4
%A _Gary W. Adamson_, Nov 22 2006
%E Edited by _N. J. A. Sloane_, Nov 29 2006
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