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 A169603 #26 Mar 13 2022 03:25:19
%S A169603 0,0,7,0,11,24,0,15,32,51,0,19,40,63,88,0,23,48,75,104,135,0,27,56,87,
%T A169603 120,155,192,0,31,64,99,136,175,216,259,0,35,72,111,152,195,240,287,
%U A169603 336,0,39,80,123,168,215,264,315,368,423,0,43,88,135,184,235,288,343,400,459,520
%N A169603 Triangle T(n,k) = k*(4*n+k+2), read by rows.
%C A169603 These are the numerators of 1/(2*n+1)^2 - 1/(2*n+k+1)^2 as they appear in the energies of the hydrogen spectrum, not reduced by common factors with the denominators.
%D A169603 Charles Janet, Considérations sur la structure du noyau de l'atome, Décembre 1929, N 5, Beauvais, page 39.
%H A169603 G. C. Greubel, <a href="/A169603/b169603.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A169603 T(n,k) = k*(4*n+k+2).
%F A169603 Sum_{k=0..n} T(n,k) = A169607(n) = 7*A000330(n), 7 times the sum of squares.
%e A169603 The array begins as:
%e A169603 0, 3, 8, 15, 24, 35, 48, 63, 80 ... A005563;
%e A169603 0, 7, 16, 27, 40, 55, 72, 91, 112 ... A028560;
%e A169603 0, 11, 24, 39, 56, 75, 96, 119, 144 ... A098603;
%e A169603 0, 15, 32, 51, 72, 95, 120, 147, 176 ... A098848;
%e A169603 0, 19, 40, 63, 88, 115, 144, 175, 208 ... A098850;
%e A169603 0, 23, 48, 75, 104, 135, 168, 203, 240 ... A132764;
%e A169603 0, 27, 56, 87, 120, 155, 192, 231, 272 ... A132768;
%e A169603 0, 31, 64, 99, 136, 175, 216, 259, 304 ... A132772;
%e A169603 0, 35, 72, 111, 152, 195, 240, 287, 336 ...;
%e A169603 The triangle starts as:
%e A169603 0;
%e A169603 0, 7;
%e A169603 0, 11, 24;
%e A169603 0, 15, 32, 51;
%e A169603 0, 19, 40, 63, 88;
%e A169603 0, 23, 48, 75, 104, 135;
%e A169603 0, 27, 56, 87, 120, 155, 192;
%e A169603 0, 31, 64, 99, 136, 175, 216, 259;
%e A169603 0, 35, 72, 111, 152, 195, 240, 287, 336;
%e A169603 0, 39, 80, 123, 168, 215, 264, 315, 368, 423;
%e A169603 0, 43, 88, 135, 184, 235, 288, 343, 400, 459, 520;
%t A169603 Table[k(4n+2+k),{n,0,10},{k,0,n}]//Flatten (* _Harvey P. Dale_, Aug 08 2021 *)
%o A169603 (Magma) [k*(4*n+k+2): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Mar 13 2022
%o A169603 (Sage) flatten([[k*(4*n+k+2) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Mar 13 2022
%Y A169603 Cf. A169607 (row sums).
%Y A169603 Cf. A005563, A028560, A098603, A098848, A098850, A132764, A132768, A132772.
%K A169603 nonn,frac,tabl
%O A169603 0,3
%A A169603 _Paul Curtz_, Dec 03 2009