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 A381603 #10 Mar 01 2025 08:35:59 %S A381603 1,1,0,1,1,0,1,2,6,0,1,3,13,60,0,1,4,21,132,776,0,1,5,30,217,1708, %T A381603 11802,0,1,6,40,316,2814,25876,201465,0,1,7,51,430,4113,42510,439446, %U A381603 3759100,0,1,8,63,560,5625,62016,718647,8155874,75404151,0,1,9,76,707,7371,84731,1044228,13270944,162762498,1608036861,0 %N A381603 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 A120973. %F A381603 See A120973. %e A381603 Square array begins: %e A381603 1, 1, 1, 1, 1, 1, 1, ... %e A381603 0, 1, 2, 3, 4, 5, 6, ... %e A381603 0, 6, 13, 21, 30, 40, 51, ... %e A381603 0, 60, 132, 217, 316, 430, 560, ... %e A381603 0, 776, 1708, 2814, 4113, 5625, 7371, ... %e A381603 0, 11802, 25876, 42510, 62016, 84731, 111018, ... %e A381603 0, 201465, 439446, 718647, 1044228, 1421835, 1857631, ... %o A381603 (PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(3*n+k, j)/(3*n+k)*a(n-j, 3*j))); %Y A381603 Columns k=0..1 give A000007, A120973. %Y A381603 Cf. A379598, A381602. %K A381603 nonn,tabl %O A381603 0,8 %A A381603 _Seiichi Manyama_, Mar 01 2025