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 A164915 #21 Mar 29 2023 17:43:15
%S A164915 1,1,10,1,9,100,1,8,90,1000,1,7,81,900,10000,1,6,73,810,9000,100000,1,
%T A164915 5,66,729,8100,90000,1000000,1,4,60,656,7290,81000,900000,10000000,1,
%U A164915 3,55,590,6561,72900,810000,9000000,100000000
%N A164915 Inverse of binomial matrix (10^n,1) A164899. (See A164899 for companion sequence.)
%C A164915 Alternate sum and difference of diagonal integers generates A164913.
%H A164915 G. C. Greubel, <a href="/A164915/b164915.txt">Antidiagonals n = 1..50, flattened</a>
%F A164915 From _G. C. Greubel_, Feb 10 2023: (Start)
%F A164915 A(n, k) = A(n-1, k) - A(n-1, k-1), with A(n, 1) = 1 and A(1, k) = 10^(k-1) (array).
%F A164915 T(n, k) = T(n-1, k) - T(n-2, k-1), with T(n, 1) = 1 and T(n, n) = 10^(n-1) (antidiagonal triangle).
%F A164915 Sum_{k=1..n} T(n, k) = (1/273)*(3*10^(n+1) - 15*A057079(n+1) - 12*A128834(n)).
%F A164915 Sum_{k=1..n} (-1)^(k-1)*T(n, k) = (1/109)*(4*Fibonacci(n) + 5*LucasL(n) + (-10)^(n+1)). (End)
%e A164915 Matrix array, A(n, k), begins:
%e A164915 1, 10, 100, 1000, 10000, 100000, ...
%e A164915 1, 9, 90, 900, 9000, 90000, ...
%e A164915 1, 8, 81, 810, 8100, 81000, ...
%e A164915 1, 7, 73, 729, 7290, 72900, ...
%e A164915 1, 6, 66, 656, 6561, 65610, ...
%e A164915 1, 5, 60, 590, 5905, 59049, ...
%e A164915 1, 4, 55, 530, 5315, 53144, ...
%e A164915 Antidiagonal triangle, T(n, k), begins as:
%e A164915 1;
%e A164915 1, 10;
%e A164915 1, 9, 100;
%e A164915 1, 8, 90, 1000;
%e A164915 1, 7, 81, 900, 10000;
%e A164915 1, 6, 73, 810, 9000, 100000;
%e A164915 1, 5, 66, 729, 8100, 90000, 1000000;
%t A164915 T[n_, k_]:= T[n, k]= If[k==n, 10^(n-1), If[k==1, 1, T[n-1,k] - T[n-2, k -1]]];
%t A164915 Table[T[n, k], {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Feb 10 2023 *)
%o A164915 (Magma)
%o A164915 function T(n,k) // T = A164915
%o A164915 if k eq n then return 10^(n-1);
%o A164915 elif k eq 1 then return 1;
%o A164915 else return T(n-1,k) - T(n-2,k-1);
%o A164915 end if; return T;
%o A164915 end function;
%o A164915 [T(n,k): k in [1..n], n in [1..15]]; // _G. C. Greubel_, Feb 10 2023
%o A164915 (SageMath)
%o A164915 def T(n,k): # T = A164915
%o A164915 if (k==n): return 10^(n-1)
%o A164915 elif (k==1): return 1
%o A164915 else: return T(n-1,k) - T(n-2,k-1)
%o A164915 flatten([[T(n,k) for k in range(1,n+1)] for n in range(1,16)]) # _G. C. Greubel_, Feb 10 2023
%Y A164915 Cf. A000032, A000045, A001019, A007318, A057079.
%Y A164915 Cf. A128834, A164881, A164899, A164913.
%K A164915 sign,tabl
%O A164915 1,3
%A A164915 _Mark Dols_, Aug 31 2009