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 A360665 #38 Apr 20 2023 06:41:51
%S A360665 0,0,0,0,1,-1,0,2,3,-3,0,3,7,6,-6,0,4,11,15,10,-10,0,5,15,24,26,15,
%T A360665 -15,0,6,19,33,42,40,21,-21,0,7,23,42,58,65,57,28,-28,0,8,27,51,74,90,
%U A360665 93,77,36,-36,0,9,31,60,90,115,129,126,100,45,-45
%N A360665 Square array T(n, k) = k*((2*n-1)*k+1)/2 read by rising antidiagonals.
%F A360665 T(n,k) = T(n,k-1)+k^2.
%F A360665 T(n,n) = A081436(n-1).
%F A360665 T(n,n+1) = A059270(n).
%F A360665 T(n,n+4) = -3*A179297(n+4).
%F A360665 T(n+3,n) = A162254(n).
%F A360665 T(n+5,n) = 3*A101986(n).
%F A360665 From _Stefano Spezia_, Mar 31 2023: (Start)
%F A360665 O.g.f.: (x*y - y^2 + 2*x*y^2)/((1 - x)^2*(1 - y)^3).
%F A360665 E.g.f.: exp(x+y)*y*(2*x - y + 2*x*y)/2. (End)
%e A360665 By rows:
%e A360665 0, 0, -1, -3, -6, -10, -15, -21, -28, ... = -A161680
%e A360665 0, 1, 3, 6, 10, 15, 21, 28, 36, ... = A000217
%e A360665 0, 2, 7, 15, 26, 40, 57, 77, 100, ... = A005449
%e A360665 0, 3, 11, 24, 42, 65, 93, 126, 164, ... = A005475
%e A360665 0, 4, 15, 33, 58, 90, 129, 175, 228, ... = A022265
%e A360665 0, 5, 19, 42, 74, 115, 165, 224, 292, ... = A022267
%e A360665 0, 6, 23, 51, 90, 140, 201, 273, 356, ... = A022269
%e A360665 ... .
%t A360665 T[n_, k_] := ((2*n - 1)*k^2 + k)/2; Table[T[n - k, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Amiram Eldar_, Mar 31 2023 *)
%o A360665 (PARI) T(n, k) = ((2*n-1)*k^2+k)/2 \\ _Thomas Scheuerle_, Mar 17 2023
%Y A360665 Cf. Antidiagonal sums: A034827(n+1).
%Y A360665 Cf. A000217, A000290, A005449, A005475, A022265.
%Y A360665 Cf. A022267, A022269, A059270, A081436, A101986.
%Y A360665 Cf. A161680, A162254, A179297, A360962, A361226.
%K A360665 sign,tabl,easy
%O A360665 0,8
%A A360665 _Paul Curtz_, Mar 17 2023