This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A137596 #26 Apr 09 2025 04:20:38
%S A137596 1,1,1,1,2,1,1,3,4,1,1,4,11,7,1,1,5,26,32,11,1,1,6,57,122,76,16,1,1,7,
%T A137596 120,423,426,156,22,1,1,8,247,1389,2127,1206,288,29,1,1,9,502,4414,
%U A137596 9897,8157,2934,491,37,1
%N A137596 Triangle read by rows: T(n, k) = Sum_{i=0..n} Stirling2(i, k).
%F A137596 T = A000012 * A048993 as infinite lower triangular matrices.
%F A137596 T(n, k) = Sum_{i=0..n-k} Stirling2(i+k, k). - _Igor Victorovich Statsenko_, May 25 2024
%e A137596 First few rows of the triangle:
%e A137596 1;
%e A137596 1, 1;
%e A137596 1, 2, 1;
%e A137596 1, 3, 4, 1;
%e A137596 1, 4, 11, 7, 1;
%e A137596 1, 5, 26, 32, 11, 1;
%e A137596 1, 6, 57, 122, 76, 16, 1;
%e A137596 1, 7, 120, 423, 426, 156, 22, 1;
%e A137596 ...
%p A137596 T := (n, k) -> add(Stirling2(i, k), i=0..n):
%p A137596 seq(seq(T(n, k), k=0..n), n=0..9); # _Peter Luschny_, Mar 07 2025
%Y A137596 Cf. A005001 (row sums), A048993.
%K A137596 nonn,tabl
%O A137596 0,5
%A A137596 _Gary W. Adamson_, Jan 29 2008
%E A137596 Offset set to 0 by _Peter Luschny_, May 25 2024