cp's OEIS Frontend

A125178 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.

%I A125178 #10 Feb 14 2022 01:25:06
%S A125178 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 A125178 877,279,116,67,43,22,7,1,4140,1156,395,183,110,65,29,8,1,21147,5296,
%U A125178 1551,578,293,175,94,37,9,1,115975,26443,6847,2129,871,468,269,131,46,10,1
%N A125178 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 A125178 Row sums = 1, 2, 5, 13, 36, 109, 369, ...
%C A125178 Columns 0,1 and 2 yield A000110, A005001 and A029761, respectively.
%e A125178 First few rows of the triangle:
%e A125178     1;
%e A125178     1,  1;
%e A125178     2,  2,  1;
%e A125178     5,  4,  3,  1;
%e A125178    15,  9,  7,  4,  1;
%e A125178    52, 24, 16, 11,  5, 1;
%e A125178   203, 76, 40, 27, 16, 6, 1;
%e A125178   ...
%e A125178 (4,3) = 16 = 7 + 9 = (3,3) + (3,2).
%p A125178 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 A125178 Cf. A000110, A005001, A029761.
%K A125178 nonn,tabl
%O A125178 0,4
%A A125178 _Gary W. Adamson_, Nov 22 2006
%E A125178 Edited by _N. J. A. Sloane_, Nov 29 2006