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Table of binomial coefficients mod m^2, read by rows: T(m, n) = binomial(m, n) mod m^2.
3

%I #13 Jul 30 2014 05:05:49

%S 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 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 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 Table of binomial coefficients mod m^2, read by rows: T(m, n) = binomial(m, n) mod m^2.

%C a(0) = 0 by convention.

%H Vincenzo Librandi, <a href="/A094495/b094495.txt">Rows n = 0..100, flattened</a>

%e First deviation from A007318 is at a(40) = T(8,4) because binomial(8,4)=70 and 70 mod 64 = 6.

%t Flatten[Table[Table[Mod[Binomial[n, j], n^2], {j, 0, n}], {n, 1, 20}], 1]

%o (PARI) T(m,n)=binomial(m,n)%m^2 \\ _Charles R Greathouse IV_, Jul 29 2014

%Y Cf. A007318, A053200, A094496, A094497.

%K easy,nonn,tabl

%O 0,5

%A _Labos Elemer_, Jun 02 2004