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 A050163 #12 Dec 21 2017 06:19:22
%S A050163 1,3,4,9,14,15,28,48,55,56,90,165,200,209,210,297,572,726,780,791,792,
%T A050163 1001,2002,2639,2912,2989,3002,3003,3432,7072,9620,10880,11320,11424,
%U A050163 11439,11440,11934,25194,35190,40698,42942,43605
%N A050163 T(n, k) = S(2n+2, n+2, k+2) for 0<=k<=n and n >= 0, array S as in A050157.
%F A050163 T(n, k) = Sum_{0<=j<=k} t(n, j), array t as in A050155.
%F A050163 T(n, k) = binomial(2*n+2, n) - binomial(2*n+2, n+k+3). - _Peter Luschny_, Dec 21 2017
%e A050163 Triangle starts:
%e A050163 1
%e A050163 3, 4
%e A050163 9, 14, 15
%e A050163 28, 48, 55, 56
%e A050163 90, 165, 200, 209, 210
%e A050163 297, 572, 726, 780, 791, 792
%e A050163 1001, 2002, 2639, 2912, 2989, 3002, 3003
%p A050163 A050163 := (n, k) -> binomial(2*n+2, n) - binomial(2*n+2, n+k+3):
%p A050163 seq(seq(A050163(n,k), k=0..n), n=0..8); # _Peter Luschny_, Dec 21 2017
%Y A050163 T(n, 0) = A000245(n+1).
%Y A050163 T(n, 1) = A002057(n).
%Y A050163 T(n, n) = A001791(n+1).
%Y A050163 Row sums are A000531(n+1).
%Y A050163 Cf. A050155, A050157.
%K A050163 nonn,tabl
%O A050163 0,2
%A A050163 _Clark Kimberling_