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 A047848 #15 Jan 14 2025 10:30:20
%S A047848 1,2,1,5,2,1,14,6,2,1,41,22,7,2,1,122,86,32,8,2,1,365,342,157,44,9,2,
%T A047848 1,1094,1366,782,260,58,10,2,1,3281,5462,3907,1556,401,74,11,2,1,9842,
%U A047848 21846,19532,9332,2802,586,92,12,2,1,29525,87382,97657,55988,19609,4682,821,112,13,2,1
%N A047848 Array A read by diagonals; n-th difference of (A(k,n), A(k,n-1),..., A(k,0)) is (k+2)^(n-1), for n=1,2,3,...; k=0,1,2,...
%H A047848 G. C. Greubel, <a href="/A047848/b047848.txt">Antidiagonals n = 0..50, flattened</a>
%F A047848 A(n, k) = ((n+3)^k + n + 1)/(n+2). - _Ralf Stephan_, Feb 14 2004
%F A047848 From _G. C. Greubel_, Jan 11 2025: (Start)
%F A047848 T(n, k) = ((k+3)^(n-k) + k + 1)/(k+2) (antidiagonal triangle).
%F A047848 T(n, n) = A196793(n).
%F A047848 Sum_{k=0..n} T(n, k) = A047857(n). (End)
%e A047848 Array, A(n, k), begins as:
%e A047848 1, 2, 5, 14, 41, ... = A007051.
%e A047848 1, 2, 6, 22, 86, ... = A047849.
%e A047848 1, 2, 7, 32, 157, ... = A047850.
%e A047848 1, 2, 8, 44, 260, ... = A047851.
%e A047848 1, 2, 9, 58, 401, ... = A047852.
%e A047848 1, 2, 10, 74, 586, ... = A047853.
%e A047848 1, 2, 11, 92, 821, ... = A047854.
%e A047848 1, 2, 12, 112, 1112, ... = A047855.
%e A047848 1, 2, 13, 134, 1465, ... = A047856.
%e A047848 1, 2, 14, 158, 1886, ... = A196791.
%e A047848 1, 2, 15, 184, 2381, ... = A196792.
%e A047848 Downward antidiagonals, T(n, k), begins as:
%e A047848 1;
%e A047848 2, 1;
%e A047848 5, 2, 1;
%e A047848 14, 6, 2, 1;
%e A047848 41, 22, 7, 2, 1;
%e A047848 122, 86, 32, 8, 2, 1;
%e A047848 365, 342, 157, 44, 9, 2, 1;
%e A047848 1094, 1366, 782, 260, 58, 10, 2, 1;
%e A047848 3281, 5462, 3907, 1556, 401, 74, 11, 2, 1;
%e A047848 9842, 21846, 19532, 9332, 2802, 586, 92, 12, 2, 1;
%e A047848 29525, 87382, 97657, 55988, 19609, 4682, 821, 112, 13, 2, 1;
%t A047848 A[n_, k_]:= ((n+3)^k +n+1)/(n+2);
%t A047848 A047848[n_, k_]:= A[k,n-k];
%t A047848 Table[A047848[n,k], {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Jan 11 2025 *)
%o A047848 (Magma)
%o A047848 A:= func< n,k | ((n+3)^k +n+1)/(n+2) >; // array A047848
%o A047848 [A(k,n-k): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Jan 11 2025
%o A047848 (Python)
%o A047848 def A(n,k): return (pow(n+3,k) +n+1)//(n+2) # array A047848
%o A047848 print(flatten([[A(k,n-k) for k in range(n+1)] for n in range(13)])) # _G. C. Greubel_, Jan 11 2025
%Y A047848 Cf. A047857 (row sums), A196793 (main diagonal).
%K A047848 nonn,tabl,easy
%O A047848 0,2
%A A047848 _Clark Kimberling_