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%I #15 Apr 02 2022 14:19:13
%S 1,1,1,1,2,1,1,2,4,1,1,2,5,8,1,1,2,5,14,16,1,1,2,5,15,41,32,1,1,2,5,
%T 15,51,122,64,1,1,2,5,15,52,187,365,128,1,1,2,5,15,52,202,715,1094,
%U 256,1,1,2,5,15,52,203,855,2795,3281,512,1
%N Triangle read by rows: T(n,k) = Sum_{j=1..n-k+1} Stirling2(k, j).
%C Rows of the array tend to A000110 starting (1, 2, 5, 15, 52, ...).
%H Andrew Howroyd, <a href="/A137855/b137855.txt">Table of n, a(n) for n = 1..1275</a>
%F Take antidiagonals of an array formed by A000012 * A008277(transform), where A000012 = (1; 1,1; 1,1,1; ...) and A008277 = the Stirling2 triangle.
%e First few rows of the array:
%e 1, 1, 1, 1, 1, ...
%e 1, 2, 4, 8, 16, ...
%e 1, 2, 5, 14, 41, ...
%e 1, 2, 5, 14, 51, ...
%e 1, 2, 5, 14, 52, ...
%e ...
%e First few rows of the triangle:
%e 1;
%e 1, 1;
%e 1, 2, 1;
%e 1, 2, 4, 1;
%e 1, 2, 5, 8, 1;
%e 1, 2, 5, 14, 16, 1;
%e 1, 2, 5, 15, 41, 32, 1;
%e 1, 2, 5, 15, 51, 122, 64, 1;
%e 1, 2, 5, 15, 52, 187, 365, 128, 1;
%e 1, 2, 5, 15, 52, 202, 715, 1094, 256, 1;
%e ...
%o (PARI) T(n,k)={sum(j=1, n-k+1, stirling(k,j,2))} \\ _Andrew Howroyd_, Aug 09 2018
%Y Row sums are A137856.
%Y Cf. A008277, A000110, A203647, A278984.
%K nonn,tabl
%O 1,5
%A _Gary W. Adamson_, Feb 16 2008
%E Name changed by _Andrew Howroyd_, Aug 09 2018
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