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 A265435 #12 Feb 05 2025 22:04:05
%S A265435 1,0,1,0,1,1,0,4,2,1,0,19,9,3,1,0,100,46,15,4,1,0,562,254,82,22,5,1,0,
%T A265435 3304,1476,474,128,30,6,1,0,20071,8893,2847,773,185,39,7,1,0,124996,
%U A265435 55046,17587,4796,1165,254,49,8,1,0,793774,347922,111006,30378,7461,1665,336,60,9,1
%N A265435 Riordan array (1, x*f(x)) where f(x) is the g.f. of A007564.
%C A265435 Triangle T(n,k), 0<=k<=n, read by rows, given by (0, 1, 3, 1, 3, 1, 3, 1, 3, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
%H A265435 Alois P. Heinz, <a href="/A265435/b265435.txt">Rows n = 0..140, flattened</a>
%e A265435 Triangle begins:
%e A265435 1
%e A265435 0, 1
%e A265435 0, 1, 1
%e A265435 0, 4, 2, 1
%e A265435 0, 19, 9, 3, 1
%e A265435 0, 100, 46, 15, 4, 1
%e A265435 Production matrix begins:
%e A265435 0, 1
%e A265435 0, 1, 1
%e A265435 0, 3, 1, 1
%e A265435 0, 9, 3, 1, 1
%e A265435 0, 27, 9, 3, 1, 1
%e A265435 0, 81, 27, 9, 3, 1, 1
%t A265435 f[x_]:=(1+2*x-Sqrt[1-8*x+4*x^2])/(6*x); T[n_,k_]:=SeriesCoefficient[(x*f[x])^k,{x,0,n}]; Table[T[n,k],{n,0,10},{k,0,n}]//Flatten (* _Stefano Spezia_, Feb 05 2025 *)
%Y A265435 Cf. A007564, A108524 (row sums).
%K A265435 nonn,tabl
%O A265435 0,8
%A A265435 _Philippe Deléham_, Dec 09 2015