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 A384860 #17 Jun 12 2025 08:28:57
%S A384860 1,1,0,1,1,0,1,2,7,0,1,3,16,28,0,1,4,27,98,-107,0,1,5,40,216,304,
%T A384860 -11744,0,1,6,55,388,1485,-20638,-519101,0,1,7,72,620,3712,-20592,
%U A384860 -1185920,-12366080,0,1,8,91,918,7285,-3836,-1908657,-35662030,-101065751,0
%N A384860 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of e.g.f. B(x)^k, where B(x) is the e.g.f. of A384856.
%F A384860 Let b(n,k) = 0^n if n*k=0, otherwise b(n,k) = (-1)^n * k * Sum_{j=1..n} (-2*n+2*j+k)^(j-1) * binomial(n,j) * b(n-j,3*j). Then A(n,k) = b(n,-k).
%e A384860 Square array begins:
%e A384860 1, 1, 1, 1, 1, 1, ...
%e A384860 0, 1, 2, 3, 4, 5, ...
%e A384860 0, 7, 16, 27, 40, 55, ...
%e A384860 0, 28, 98, 216, 388, 620, ...
%e A384860 0, -107, 304, 1485, 3712, 7285, ...
%e A384860 0, -11744, -20638, -20592, -3836, 39200, ...
%o A384860 (PARI) b(n, k) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, (-2*n+2*j+k)^(j-1)*binomial(n, j)*b(n-j, 3*j)));
%o A384860 a(n, k) = b(n, -k);
%Y A384860 Columns k=0..1 give A000007, A384856.
%Y A384860 Cf. A058127, A384811.
%K A384860 sign,tabl
%O A384860 0,8
%A A384860 _Seiichi Manyama_, Jun 10 2025