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 A114192 #14 Jan 17 2014 14:14:21
%S A114192 1,2,1,4,6,1,8,24,10,1,16,80,60,14,1,32,240,280,112,18,1,64,672,1120,
%T A114192 672,180,22,1,128,1792,4032,3360,1320,264,26,1,256,4608,13440,14784,
%U A114192 7920,2288,364,30,1,512,11520,42240,59136,41184,16016,3640,480,34,1
%N A114192 Riordan array (1/(1-2x),x/(1-2x)^2).
%C A114192 Factors as (1/(1-x),x/(1-x))*(1/(1-x),x*(1+x)/(1-x)^2) or A007318 times A114188. Also (1/(1-2*x),x/(1-2*x))*(1,x*(1+2*x)). Inverse is A114193. Row sums are A007583. Diagonal sums are A007051.
%F A114192 T(n,k) = sum{j=0..n, C(k, j)*C(n, k+j)}*2^(n-k).
%F A114192 T(n,k) = 2^(n-k)*binomial(n+k,2k) = 2^(n-k)*A085478(n,k). - _Philippe Deléham_, May 05 2006
%F A114192 T(n,k) = A013609(n+k, n-k). - _Johannes W. Meijer_, Sep 05 2013
%F A114192 T(n,k) = 4*T(n-1,k) + T(n-1,k-1) - 4*T(n-2,k), T(0,0) = T(1,1) = 1, T(1,0) = 2, T(n,k) = 0 if k<0 or if k>n. - _Philippe Deléham_, Jan 17 2014
%e A114192 Triangle begins
%e A114192 1;
%e A114192 2, 1;
%e A114192 4, 6, 1;
%e A114192 8, 24, 10, 1;
%e A114192 16, 80, 60, 14, 1;
%e A114192 32, 240, 280, 112, 18, 1;
%K A114192 easy,nonn,tabl
%O A114192 0,2
%A A114192 _Paul Barry_, Nov 16 2005