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 A156286 #6 Sep 08 2022 08:45:41 %S A156286 1,1,10,1,140,1419,1,5740,242649,3350536,1,700280,165729267, %T A156286 7853656384,161827775045,1,255602200,452606628177,92036999164096, %U A156286 6040221703554625,193317016162131576,1,279628806800,4943822199577371,5392815929021041024,1352701610289354714125,132670761753844630766736,6731905265314349384346775 %N A156286 Triangle T(n, k) = (1/k^n)*Product_{j=1..n} ( (k-1)*(k+1)^j + 1 ), read by rows. %H A156286 G. C. Greubel, <a href="/A156286/b156286.txt">Rows n = 1..25 of the triangle, flattened</a> %F A156286 T(n, k) = Product_{j=1..n} ( (k+1)^j - Sum_{i=0..k-1} (k+1)^i ). %F A156286 T(n, k) = (1/k^n)*Product_{j=1..n} ( (k-1)*(k+1)^j + 1 ). - _G. C. Greubel_, Jan 02 2022 %e A156286 Triangle begins as: %e A156286 1; %e A156286 1, 10; %e A156286 1, 140, 1419; %e A156286 1, 5740, 242649, 3350536; %e A156286 1, 700280, 165729267, 7853656384, 161827775045; %t A156286 T[n_, k_]:= (1/k^n)*Product[(k-1)*(k+1)^j +1, {j,n}]; %t A156286 Table[T[n, k], {n, 10}, {k, n}]//Flatten (* modified by _G. C. Greubel_, Jan 02 2022 *) %o A156286 (Magma) A156286:= func< n,k | (&*[(k-1)*(k+1)^j + 1: j in [1..n]])/k^n >; %o A156286 [A156286(n,k): k in [1..n], n in [1..10]]; // _G. C. Greubel_, Jan 02 2022 %o A156286 (Sage) %o A156286 def A156286(n,k): return (1/k^n)*product( (k-1)*(k+1)^j +1 for j in (1..n) ) %o A156286 flatten([[A156286(n,k) for k in (1..n)] for n in (1..10)]) # _G. C. Greubel_, Jan 02 2022 %Y A156286 Cf. A156173. %K A156286 nonn,tabl %O A156286 1,3 %A A156286 _Roger L. Bagula_, Feb 07 2009 %E A156286 Edited by _G. C. Greubel_, Jan 02 2022