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 A384583 #11 Jun 04 2025 09:54:09
%S A384583 1,1,0,1,1,0,1,2,1,0,1,3,3,6,0,1,4,6,14,31,0,1,5,10,25,75,236,0,1,6,
%T A384583 15,40,135,546,2166,0,1,7,21,60,215,951,4902,22722,0,1,8,28,86,320,
%U A384583 1476,8338,50620,269889,0,1,9,36,119,456,2151,12634,84714,593347,3567412,0
%N A384583 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 A384575.
%F A384583 A(n,0) = 0^n; A(n,k) = k * Sum_{j=0..n} binomial(5*n-5*j+k,j)/(5*n-5*j+k) * A(n-j,j).
%e A384583 Square array begins:
%e A384583 1, 1, 1, 1, 1, 1, 1, ...
%e A384583 0, 1, 2, 3, 4, 5, 6, ...
%e A384583 0, 1, 3, 6, 10, 15, 21, ...
%e A384583 0, 6, 14, 25, 40, 60, 86, ...
%e A384583 0, 31, 75, 135, 215, 320, 456, ...
%e A384583 0, 236, 546, 951, 1476, 2151, 3012, ...
%e A384583 0, 2166, 4902, 8338, 12634, 17985, 24627, ...
%o A384583 (PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(5*n-5*j+k, j)/(5*n-5*j+k)*a(n-j, j)));
%Y A384583 Columns k=0..1 give A000007, A384575.
%Y A384583 Cf. A381566, A384580, A384581, A384582.
%K A384583 nonn,tabl
%O A384583 0,8
%A A384583 _Seiichi Manyama_, Jun 04 2025