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 A103219 #10 Sep 01 2024 00:13:11
%S A103219 1,10,3,35,18,5,84,53,26,7,165,116,71,34,9,286,215,148,89,42,11,455,
%T A103219 358,265,180,107,50,13,680,553,430,315,212,125,58,15,969,808,651,502,
%U A103219 365,244,143,66,17,1330,1131,936,749,574,415,276,161,74,19,1771,1530,1293
%N A103219 Triangle read by rows: T(n,k) = (n+1-k)*(4*(n+1-k)^2 - 1)/3+2*k*(n+1-k)^2.
%C A103219 The triangle is generated from the product B * A of the infinite lower triangular matrices A =
%C A103219 1 0 0 0...
%C A103219 3 1 0 0...
%C A103219 5 3 1 0...
%C A103219 7 5 3 1...
%C A103219 ...
%C A103219 and B =
%C A103219 1 0 0 0...
%C A103219 1 3 0 0...
%C A103219 1 3 5 0...
%C A103219 1 3 5 7...
%C A103219 ...
%e A103219 Triangle begins:
%e A103219 1,
%e A103219 10,3,
%e A103219 35,18,5,
%e A103219 84,53,26,7,
%e A103219 165,116,71,34,9,
%e A103219 286,215,148,89,42,11,
%t A103219 T[n_, k_] := (n + 1 - k)*(4*(n + 1 - k)^2 - 1)/3 + 2*k*(n + 1 - k)^2; Flatten[ Table[ T[n, k], {n, 0, 10}, {k, 0, n}]] (* _Robert G. Wilson v_, Feb 10 2005 *)
%o A103219 (PARI) T(n,k)=(n+1-k)*(4*(n+1-k)^2-1)/3+2*k*(n+1-k)^2; for(i=0,10, for(j=0,i,print1(T(i,j),","));print())
%Y A103219 Row sums give A103220.
%Y A103219 T(n, 0) = (n+1)*(4*(n+1)^2 - 1)/3 = A000447(n+1);
%Y A103219 T(n+1, n)= 8*n+2 = A017089(n+1);
%Y A103219 Cf. A103218 (for product A*B), A103220.
%K A103219 nonn,tabl,easy
%O A103219 0,2
%A A103219 Lambert Klasen (lambert.klasen(AT)gmx.de) and _Gary W. Adamson_, Jan 26 2005