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 A094496 #11 Dec 12 2024 14:54:51 %S A094496 1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, %T A094496 0,0,0,0,0,0,64,0,0,0,0,0,0,0,81,81,81,81,0,0,0,0,0,0,100,200,200,200, %U A094496 100,0,0,0,0,0,0,121,242,363,363,242,121,0,0,0,0,0,0,144,432,720,864,720,432,144,0,0,0 %N A094496 Triangle read by rows: T(n,k) = binomial(n,k) - binomial(n,k) mod n^2, with T(0,0) = 1. %H A094496 Andrew Howroyd, <a href="/A094496/b094496.txt">Table of n, a(n) for n = 0..1325</a> (rows 0..50) %F A094496 T(n,k) = A007318(n,k) - A094495(n,k). %e A094496 Triangle begins: %e A094496 1; %e A094496 1, 1; %e A094496 0, 0, 0; %e A094496 0, 0, 0, 0; %e A094496 0, 0, 0, 0, 0; %e A094496 0, 0, 0, 0, 0, 0; %e A094496 0, 0, 0, 0, 0, 0, 0; %e A094496 0, 0, 0, 0, 0, 0, 0, 0; %e A094496 0, 0, 0, 0, 64, 0, 0, 0, 0; %e A094496 0, 0, 0, 81, 81, 81, 81, 0, 0, 0; %e A094496 0, 0, 0, 100, 200, 200, 200, 100, 0, 0, 0; %e A094496 ... %e A094496 T(8,6) = binomial(8,4) - binomial(8,4) mod 8^2 = 70 - 6 = 64. %t A094496 Flatten[Table[Table[Binomial[n, j]-Mod[Binomial[n, j], n^2], {j, 0, n}], {n, 1, 20}], 1] %o A094496 (PARI) T(n,k) = my(x=binomial(n,k)); x - if(n, x % n^2) \\ _Andrew Howroyd_, Dec 12 2024 %Y A094496 Cf. A007318, A053200, A094495, A094497. %K A094496 easy,nonn,tabl,less %O A094496 0,41 %A A094496 _Labos Elemer_, Jun 02 2004