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 A128417 #15 Jul 29 2025 21:05:19
%S A128417 1,4,1,24,8,1,160,60,12,1,1120,448,112,16,1,8064,3360,960,180,20,1,
%T A128417 59136,25344,7920,1760,264,24,1,439296,192192,64064,16016,2912,364,28,
%U A128417 1,3294720,1464320,512512,139776,29120,4480,480,32,1
%N A128417 Number triangle T(n,k) = 2^(n-k)*C(2*n,n-k).
%C A128417 Inverse of A128414. Row sums are A128418. Diagonal sums are A128419.
%H A128417 Sheng-Liang Yang, Yan-Ni Dong, and Tian-Xiao He, <a href="https://doi.org/10.1016/j.disc.2017.07.006">Some matrix identities on colored Motzkin paths</a>, Discrete Mathematics 340.12 (2017): 3081-3091.
%F A128417 Riordan array (1/sqrt(1-8*x),(1-4*x-sqrt(1-8*x))/(8*x)).
%F A128417 T(n,k) = 2^(n-k)*A094527(n,k).
%e A128417 Triangle begins:
%e A128417 1,
%e A128417 4, 1,
%e A128417 24, 8, 1,
%e A128417 160, 60, 12, 1,
%e A128417 1120, 448, 112, 16, 1,
%e A128417 8064, 3360, 960, 180, 20, 1,
%e A128417 59136, 25344, 7920, 1760, 264, 24, 1,
%e A128417 439296, 192192, 64064, 16016, 2912, 364, 28, 1
%e A128417 ...
%t A128417 Flatten[Table[2^(n-k) Binomial[2n,n-k],{n,0,10},{k,0,n}]] (* _Harvey P. Dale_, Nov 02 2011 *)
%Y A128417 Cf. A128413.
%K A128417 easy,nonn,tabl
%O A128417 0,2
%A A128417 _Paul Barry_, Mar 02 2007