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 A059473 #20 Nov 26 2021 16:47:18
%S A059473 1,2,2,4,10,4,8,32,32,8,16,88,148,88,16,32,224,536,536,224,32,64,544,
%T A059473 1696,2440,1696,544,64,128,1280,4928,9344,9344,4928,1280,128,256,2944,
%U A059473 13504,31936,42256,31936,13504,2944,256,512,6656,35456,100736,167072,167072,100736,35456,6656,512
%N A059473 Triangle T(n, k) is coefficient of z^n*w^k in 1/(1 - 2*z - 2*w - 2*z*w) read by rows in order 00, 10, 01, 20, 11, 02, ...
%H A059473 G. C. Greubel, <a href="/A059473/b059473.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F A059473 G.f.: 1/(1 - 2*z - 2*w - 2*z*w).
%F A059473 T(n, k) = Sum_{j=0..n} 2^(n + k - j)*binomial(n, j)*binomial(n + k - j, n). - _G. C. Greubel_, Oct 04 2017
%F A059473 T(n, k) = 2^n*binomial(n, k)*hypergeom([-k, k - n], [-n], -1/2). - _Peter Luschny_, Nov 26 2021
%e A059473 [0] 1;
%e A059473 [1] 2, 2;
%e A059473 [2] 4, 10, 4;
%e A059473 [3] 8, 32, 32, 8;
%e A059473 [4] 16, 88, 148, 88, 16;
%e A059473 [5] 32, 224, 536, 536, 224, 32;
%e A059473 [6] 64, 544, 1696, 2440, 1696, 544, 64;
%e A059473 ...
%p A059473 read transforms; SERIES2(1/(1-2*z-2*w-2*z*w),x,y,12): SERIES2TOLIST(%,x,y,12);
%p A059473 # Alternative:
%p A059473 T := (n, k) -> 2^n*binomial(n, k)*hypergeom([-k, -n + k], [-n], -1/2):
%p A059473 for n from 0 to 10 do seq(simplify(T(n, k)), k = 0 .. n) end do; # _Peter Luschny_, Nov 26 2021
%t A059473 T[n_, k_] := Sum[2^(n + k - j)*Binomial[n, j]*Binomial[n + k - j, n], {j, 0, n}]; Table[T[n - k, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _G. C. Greubel_, Oct 04 2017 *)
%Y A059473 Column k = 0 gives A000079.
%Y A059473 T(n, n) gives A098270.
%K A059473 nonn,tabl,easy
%O A059473 0,2
%A A059473 _N. J. A. Sloane_, Feb 03 2001