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 A152572 #12 Jun 02 2025 01:14:42
%S A152572 -1,1,-1,5,-1,-1,25,-5,-1,-1,125,-25,-5,-1,-1,625,-125,-25,-5,-1,-1,
%T A152572 3125,-625,-125,-25,-5,-1,-1,15625,-3125,-625,-125,-25,-5,-1,-1,78125,
%U A152572 -15625,-3125,-625,-125,-25,-5,-1,-1,390625,-78125,-15625,-3125,-625,-125,-25,-5,-1,-1
%N A152572 Triangle T(n,k) read by rows: T(n,n) = -1, T(n,0) = 5^(n - 1), T(n,k) = -5^(n - k - 1), 1 <= k <= n - 1.
%F A152572 From _Franck Maminirina Ramaharo_, Jan 08 2019: (Start)
%F A152572 G.f.: -(1 - 6*y + 2*x*y^2)/(1 - (5 + x)*y + 5*x*y^2).
%F A152572 E.g.f.: -(10 - 2*x - (5 - 2*x)*exp(5*y) + (20 - 5*x)*exp(x*y))/(25 - 5*x). (End)
%e A152572 Triangle begins:
%e A152572 -1;
%e A152572 1, -1;
%e A152572 5, -1, -1;
%e A152572 25, -5, -1, -1;
%e A152572 125, -25, -5, -1, -1;
%e A152572 625, -125, -25, -5, -1, -1;
%e A152572 3125, -625, -125, -25, -5, -1, -1;
%e A152572 15625, -3125, -625, -125, -25, -5, -1, -1;
%e A152572 78125, -15625, -3125, -625, -125, -25, -5, -1, -1;
%e A152572 390625, -78125, -15625, -3125, -625, -125, -25, -5, -1, -1;
%e A152572 1953125, -390625, -78125, -15625, -3125, -625, -125, -25, -5, -1, -1;
%e A152572 ...
%t A152572 b[0] = {-1}; b[1] = {1, -1};
%t A152572 b[n_] := b[n] = Join[{5^(n - 1)}, {-b[n - 1][[1]]}, Table[b[n - 1][[i]], {i, 2, Length[b[n - 1]]}]];
%t A152572 Flatten[Table[b[n], {n, 0, 10}]]
%o A152572 (Maxima)
%o A152572 T(n, k) := if k = n then -1 else if k = 0 then 5^(n - 1) else -5^(n - k - 1);
%o A152572 create_list(T(n, k), n, 0, 20, k, 0, n); /* _Franck Maminirina Ramaharo_, Jan 08 2019 */
%Y A152572 Row sums (except row 0): A125833.
%Y A152572 Cf. A057728, A152568, A152570, A152571.
%K A152572 sign,easy,tabl
%O A152572 0,4
%A A152572 _Roger L. Bagula_, Dec 08 2008
%E A152572 Edited by _Franck Maminirina Ramaharo_, Jan 08 2019