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 A362125 #16 Apr 01 2025 12:10:02
%S A362125 1,1,0,1,1,0,1,2,2,0,1,3,7,3,0,1,4,15,18,5,0,1,5,26,55,47,8,0,1,6,40,
%T A362125 124,198,118,13,0,1,7,57,235,571,681,290,21,0,1,8,77,398,1320,2500,
%U A362125 2263,702,34,0,1,9,100,623,2640,7026,10504,7341,1677,55,0
%N A362125 Square array T(n,k), n>=0, k>=0, read by antidiagonals downwards, where column k is the expansion of 1/(1 - x*(1+x)^k)^k.
%F A362125 T(n,k) = Sum_{j=0..n} (-1)^j * binomial(-k,j) * binomial(k*j,n-j) = Sum_{j=0..n} binomial(j+k-1,j) * binomial(k*j,n-j).
%e A362125 Square array begins:
%e A362125 1, 1, 1, 1, 1, 1, ...
%e A362125 0, 1, 2, 3, 4, 5, ...
%e A362125 0, 2, 7, 15, 26, 40, ...
%e A362125 0, 3, 18, 55, 124, 235, ...
%e A362125 0, 5, 47, 198, 571, 1320, ...
%e A362125 0, 8, 118, 681, 2500, 7026, ...
%o A362125 (PARI) T(n, k) = sum(j=0, n, binomial(j+k-1, j)*binomial(k*j, n-j));
%Y A362125 Columns k=0..3 give A000007, A000045(n+1), A362126, A382614.
%Y A362125 Main diagonal gives A362080.
%Y A362125 Cf. A362078, A362079.
%K A362125 nonn,tabl
%O A362125 0,8
%A A362125 _Seiichi Manyama_, Apr 08 2023