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 A094495 #16 Apr 30 2025 15:05:02
%S A094495 0,0,0,1,2,1,1,3,3,1,1,4,6,4,1,1,5,10,10,5,1,1,6,15,20,15,6,1,1,7,21,
%T A094495 35,35,21,7,1,1,8,28,56,6,56,28,8,1,1,9,36,3,45,45,3,36,9,1,1,10,45,
%U A094495 20,10,52,10,20,45,10,1,1,11,55,44,88,99,99,88,44,55,11,1,1,12,66,76,63,72,60,72,63,76,66,12,1
%N A094495 Table of binomial coefficients mod m^2, read by rows: T(m, n) = binomial(m, n) mod m^2.
%C A094495 a(0) = 0 by convention.
%H A094495 Vincenzo Librandi, <a href="/A094495/b094495.txt">Rows n = 0..100, flattened</a>
%e A094495 First deviation from A007318 is at a(40) = T(8,4) because binomial(8,4)=70 and 70 mod 64 = 6.
%t A094495 Flatten[Table[Table[Mod[Binomial[n, j], n^2], {j, 0, n}], {n, 1, 20}], 1]
%o A094495 (PARI) T(m,n)=binomial(m,n)%m^2 \\ _Charles R Greathouse IV_, Jul 29 2014
%o A094495 (Python)
%o A094495 from math import comb, isqrt
%o A094495 def A094495(n): return comb(r:=(m:=isqrt(k:=n+1<<1))-(k<=m*(m+1)),n-comb(r+1,2))%(r**2) if n else 0 # _Chai Wah Wu_, Apr 30 2025
%Y A094495 Cf. A007318, A053200, A094496, A094497.
%K A094495 easy,nonn,tabl
%O A094495 0,5
%A A094495 _Labos Elemer_, Jun 02 2004