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 A167172 #10 Jun 05 2016 23:48:40
%S A167172 1,1,1,1,2,1,1,3,3,1,1,4,7,4,1,1,5,11,11,5,1,1,6,16,25,16,6,1,1,7,22,
%T A167172 40,40,22,7,1,1,8,29,61,93,61,29,8,1,1,9,37,89,149,149,89,37,9,1,1,10,
%U A167172 46,125,233,371,233,125,46,10,1
%N A167172 Triangle T(n,k) read by rows: T(n,k) = binomial(n, k) + A140356(n, k) - 1.
%C A167172 Row sums are: {1, 2, 4, 8, 17, 34, 71, 140, 291, 570, 1201,...}.
%H A167172 G. C. Greubel, <a href="/A167172/b167172.txt">Table of n, a(n) for the first 50 rows</a>
%F A167172 T(n,k) = binomial(n, k) + A140356(n, k) - 1 = binomial(n, k) + if(k less than equal floor(n/2), Gamma(k + 1), Gamma(n - k + 1)) - 1.
%e A167172 {1},
%e A167172 {1, 1},
%e A167172 {1, 2, 1},
%e A167172 {1, 3, 3, 1},
%e A167172 {1, 4, 7, 4, 1},
%e A167172 {1, 5, 11, 11, 5, 1},
%e A167172 {1, 6, 16, 25, 16, 6, 1},
%e A167172 {1, 7, 22, 40, 40, 22, 7, 1},
%e A167172 {1, 8, 29, 61, 93, 61, 29, 8, 1},
%e A167172 {1, 9, 37, 89, 149, 149, 89, 37, 9, 1},
%e A167172 {1, 10, 46, 125, 233, 371, 233, 125, 46, 10, 1}.
%t A167172 t[n_, k_] = Binomial[n, k] + If[k <= Floor[n/2], Gamma[k + 1], Gamma[n - k + 1]] - 1; Flatten[Table[Table[t[n, k], {k, 0, n}], {n, 0, 10}]]
%Y A167172 Cf. A140356.
%K A167172 nonn,tabl
%O A167172 0,5
%A A167172 _Roger L. Bagula_, Oct 29 2009
%E A167172 Edited by the OEIS editors, Jun 05 2016