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 A384623 #10 Jun 05 2025 09:55:23
%S A384623 1,1,0,1,1,0,1,2,7,0,1,3,15,75,0,1,4,24,164,989,0,1,5,34,268,2177,
%T A384623 14822,0,1,6,45,388,3585,32672,242833,0,1,7,57,525,5235,53922,534781,
%U A384623 4253818,0,1,8,70,680,7150,78972,882304,9349160,78573475,0,1,9,84,854,9354,108251,1292456,15399930,172255669,1516124048,0
%N A384623 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 A384622.
%F A384623 A(n,0) = 0^n; A(n,k) = k * Sum_{j=0..n} binomial(n+j+k,j)/(n+j+k) * A(n-j,5*j).
%e A384623 Square array begins:
%e A384623 1, 1, 1, 1, 1, 1, 1, ...
%e A384623 0, 1, 2, 3, 4, 5, 6, ...
%e A384623 0, 7, 15, 24, 34, 45, 57, ...
%e A384623 0, 75, 164, 268, 388, 525, 680, ...
%e A384623 0, 989, 2177, 3585, 5235, 7150, 9354, ...
%e A384623 0, 14822, 32672, 53922, 78972, 108251, 142218, ...
%e A384623 0, 242833, 534781, 882304, 1292456, 1772920, 2332044, ...
%o A384623 (PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(n+j+k, j)/(n+j+k)*a(n-j, 5*j)));
%Y A384623 Columns k=0..1 give A000007, A384622.
%Y A384623 Cf. A379599, A384619, A384620, A384621.
%K A384623 nonn,tabl
%O A384623 0,8
%A A384623 _Seiichi Manyama_, Jun 05 2025