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 A329708 #40 Feb 15 2025 15:51:10
%S A329708 1,1,4,4,1,4,10,12,9,1,4,10,20,25,24,16,1,4,10,20,35,44,46,40,25,1,4,
%T A329708 10,20,35,56,70,76,73,60,36,1,4,10,20,35,56,84,104,115,116,106,84,49,
%U A329708 1,4,10,20,35,56,84,120,147,164,170,164,145,112,64
%N A329708 Triangle, read by rows, where the n-th row lists the (2n+1) coefficients of (1+2*x+...+(n+1)*x^n)^2.
%H A329708 Seiichi Manyama, <a href="/A329708/b329708.txt">Rows n = 0..99, flattened</a>
%F A329708 T(n,k) = A000292(k+1) for k=0..n.
%F A329708 Sum_{k=0..2n} (-1)^k * T(n,k) = A008794(n+2). - _Alois P. Heinz_, Feb 14 2025
%e A329708 Triangle begins:
%e A329708 1;
%e A329708 1, 4, 4;
%e A329708 1, 4, 10, 12, 9;
%e A329708 1, 4, 10, 20, 25, 24, 16;
%e A329708 1, 4, 10, 20, 35, 44, 46, 40, 25;
%e A329708 ...
%t A329708 row[n_]:=CoefficientList[Series[(Sum[(i+1)x^i,{i,0,n}])^2,{x,0,2n}],x]; Array[row,8,0]//Flatten (* _Stefano Spezia_, Feb 15 2025 *)
%o A329708 (PARI) for(n=0, 10, print(Vecrev(sum(k=0, n, (k+1)*x^k)^2), ", "))
%Y A329708 Row sums give A000537(n+1).
%Y A329708 T(n,2n) gives A000290(n+1).
%Y A329708 Cf. A000292, A002260, A084608, A008794, A329709.
%K A329708 nonn,tabf
%O A329708 0,3
%A A329708 _Seiichi Manyama_, Feb 29 2020