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 A381594 #16 Mar 01 2025 08:36:21
%S A381594 1,1,0,1,1,0,1,2,7,0,1,3,15,79,0,1,4,24,172,1134,0,1,5,34,280,2475,
%T A381594 18953,0,1,6,45,404,4044,41280,353134,0,1,7,57,545,5863,67365,766291,
%U A381594 7154751,0,1,8,70,704,7955,97620,1246534,15460284,155181240,0,1,9,84,882,10344,132486,1801536,25051422,333896388,3565276582,0
%N A381594 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 A381601.
%F A381594 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 A381594 Square array begins:
%e A381594 1, 1, 1, 1, 1, 1, 1, ...
%e A381594 0, 1, 2, 3, 4, 5, 6, ...
%e A381594 0, 7, 15, 24, 34, 45, 57, ...
%e A381594 0, 79, 172, 280, 404, 545, 704, ...
%e A381594 0, 1134, 2475, 4044, 5863, 7955, 10344, ...
%e A381594 0, 18953, 41280, 67365, 97620, 132486, 172434, ...
%e A381594 0, 353134, 766291, 1246534, 1801536, 2439615, 3169770, ...
%o A381594 (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 A381594 Columns k=0..1 give A000007, A381601.
%Y A381594 Cf. A379599, A381573, A381592.
%K A381594 nonn,tabl
%O A381594 0,8
%A A381594 _Seiichi Manyama_, Mar 01 2025