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First differences of n^k.
4

%I #23 Dec 21 2022 22:13:02

%S 1,1,0,1,1,0,1,2,2,0,1,3,6,4,0,1,4,12,18,8,0,1,5,20,48,54,16,0,1,6,30,

%T 100,192,162,32,0,1,7,42,180,500,768,486,64,0,1,8,56,294,1080,2500,

%U 3072,1458,128,0,1,9,72,448,2058,6480,12500,12288,4374,256,0,1,10,90,648

%N First differences of n^k.

%C T(n,k) is the number of k-digit numbers in base n; n,k >= 2. - _Mohammed Yaseen_, Nov 11 2022

%F T(n,k) = (n-1)*n^(k-1) + 0^k/n. - Corrected by _Mohammed Yaseen_, Nov 11 2022

%F T(n,0) = 1; T(n,k) = n^k - n^(k-1) for k >= 1. - _Mohammed Yaseen_, Nov 11 2022

%e Rows begin

%e 1, 0, 0, 0, 0, ...

%e 1, 1, 2, 4, 8, ...

%e 1, 2, 6, 18, 54, ...

%e 1, 3, 12, 48, 192, ...

%e 1, 4, 20, 100, 500, ...

%Y Rows include A011782, A025192, A002001, A005054, A052934, A055272, A055274, A055275, A052268, A055276.

%Y Diagonals include A053506, A085389, A085390.

%Y Row-wise binomial transform is A083064.

%K easy,nonn,tabl

%O 1,8

%A _Paul Barry_, Jun 30 2003

%E Offset corrected by _Mohammed Yaseen_, Nov 11 2022