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 A384681 #11 Jun 07 2025 08:21:18
%S A384681 1,1,0,1,1,0,1,2,3,0,1,3,7,15,0,1,4,12,36,100,0,1,5,18,64,239,805,0,1,
%T A384681 6,25,100,426,1900,7442,0,1,7,33,145,671,3357,17319,76750,0,1,8,42,
%U A384681 200,985,5260,30228,176214,866818,0,1,9,52,266,1380,7706,46880,303687,1965938,10586499,0
%N A384681 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 A384680.
%F A384681 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,j).
%e A384681 Square array begins:
%e A384681 1, 1, 1, 1, 1, 1, 1, ...
%e A384681 0, 1, 2, 3, 4, 5, 6, ...
%e A384681 0, 3, 7, 12, 18, 25, 33, ...
%e A384681 0, 15, 36, 64, 100, 145, 200, ...
%e A384681 0, 100, 239, 426, 671, 985, 1380, ...
%e A384681 0, 805, 1900, 3357, 5260, 7706, 10806, ...
%e A384681 0, 7442, 17319, 30228, 46880, 68115, 94918, ...
%o A384681 (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, j)));
%Y A384681 Columns k=0..1 give A000007, A384680.
%Y A384681 Cf. A384581, A384652.
%K A384681 nonn,tabl
%O A384681 0,8
%A A384681 _Seiichi Manyama_, Jun 06 2025