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 A361830 #20 Mar 26 2023 11:14:50
%S A361830 1,1,2,1,2,6,1,2,8,20,1,2,10,32,70,1,2,12,46,136,252,1,2,14,62,226,
%T A361830 592,924,1,2,16,80,342,1136,2624,3432,1,2,18,100,486,1932,5810,11776,
%U A361830 12870,1,2,20,122,660,3030,11094,30080,53344,48620
%N A361830 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} binomial(2*j,j) * binomial(k*j,n-j).
%F A361830 G.f. of column k: 1/sqrt(1 - 4*x*(1+x)^k).
%F A361830 n*T(n,k) = 2 * Sum_{j=0..k} binomial(k,j)*(2*n-1-j)*T(n-1-j,k) for n > k.
%e A361830 Square array begins:
%e A361830 1, 1, 1, 1, 1, 1, ...
%e A361830 2, 2, 2, 2, 2, 2, ...
%e A361830 6, 8, 10, 12, 14, 16, ...
%e A361830 20, 32, 46, 62, 80, 100, ...
%e A361830 70, 136, 226, 342, 486, 660, ...
%e A361830 252, 592, 1136, 1932, 3030, 4482, ...
%o A361830 (PARI) T(n, k) = sum(j=0, n, binomial(2*j, j)*binomial(k*j, n-j));
%Y A361830 Columns k=0..5 give A000984, A006139, A137635, A361812, A361813, A361814.
%Y A361830 Main diagonal gives A361829.
%Y A361830 Cf. A099233, A361834.
%K A361830 nonn,tabl
%O A361830 0,3
%A A361830 _Seiichi Manyama_, Mar 26 2023