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 A381648 #12 Mar 03 2025 09:32:26
%S A381648 1,1,0,1,1,0,1,2,5,0,1,3,11,44,0,1,4,18,98,510,0,1,5,26,163,1133,7024,
%T A381648 0,1,6,35,240,1884,15508,109362,0,1,7,45,330,2779,25659,239808,
%U A381648 1871530,0,1,8,56,434,3835,37704,394313,4076904,34590180,0,1,9,68,553,5070,51891,576178,6661602,74895252,682396379,0
%N A381648 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A381649.
%F A381648 A(n,0) = 0^n; A(n,k) = k * Sum_{j=0..n} binomial(3*n-j+k,j)/(3*n-j+k) * A(n-j,3*j).
%e A381648 Square array begins:
%e A381648 1, 1, 1, 1, 1, 1, 1, ...
%e A381648 0, 1, 2, 3, 4, 5, 6, ...
%e A381648 0, 5, 11, 18, 26, 35, 45, ...
%e A381648 0, 44, 98, 163, 240, 330, 434, ...
%e A381648 0, 510, 1133, 1884, 2779, 3835, 5070, ...
%e A381648 0, 7024, 15508, 25659, 37704, 51891, 68490, ...
%e A381648 0, 109362, 239808, 394313, 576178, 789055, 1036973, ...
%o A381648 (PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(3*n-j+k, j)/(3*n-j+k)*a(n-j, 3*j)));
%Y A381648 Columns k=0..1 give A000007, A381649.
%Y A381648 Cf. A381594, A381603.
%K A381648 nonn,tabl
%O A381648 0,8
%A A381648 _Seiichi Manyama_, Mar 03 2025