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 A381592 #23 Mar 03 2025 10:42:12
%S A381592 1,1,0,1,1,0,1,2,5,0,1,3,11,39,0,1,4,18,88,383,0,1,5,26,148,869,4360,
%T A381592 0,1,6,35,220,1473,9876,55201,0,1,7,45,305,2211,16740,124473,758877,0,
%U A381592 1,8,56,404,3100,25164,210260,1701630,11157081,0,1,9,68,518,4158,35381,315312,2860317,24870695,173623407,0
%N A381592 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 A381600.
%F A381592 A(n,0) = 0^n; A(n,k) = k * Sum_{j=0..n} binomial(2*n+j+k,j)/(2*n+j+k) * A(n-j,2*j).
%e A381592 Square array begins:
%e A381592 1, 1, 1, 1, 1, 1, 1, ...
%e A381592 0, 1, 2, 3, 4, 5, 6, ...
%e A381592 0, 5, 11, 18, 26, 35, 45, ...
%e A381592 0, 39, 88, 148, 220, 305, 404, ...
%e A381592 0, 383, 869, 1473, 2211, 3100, 4158, ...
%e A381592 0, 4360, 9876, 16740, 25164, 35381, 47646, ...
%e A381592 0, 55201, 124473, 210260, 315312, 442710, 595892, ...
%o A381592 (PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(2*n+j+k, j)/(2*n+j+k)*a(n-j, 2*j)));
%Y A381592 Columns k=0..2 give A000007, A381600, A381593.
%Y A381592 Cf. A379599, A381571, A381594, A381602.
%K A381592 nonn,tabl
%O A381592 0,8
%A A381592 _Seiichi Manyama_, Mar 01 2025