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A380860 Triangle read by rows: T(n,m) (0<=m<=n) = number of positive n-digit numbers that have exactly m copies of a specific, previously selected positive base-10 digit among its digits.

%I A380860 #25 Feb 07 2025 16:34:14
%S A380860 1,8,1,72,17,1,648,225,26,1,5832,2673,459,35,1,52488,29889,6804,774,
%T A380860 44,1,472392,321489,91125,13770,1170,53,1,4251528,3365793,1141614,
%U A380860 215055,24300,1647,62,1,38263752,34543665,13640319,3077109,433755,39123,2205,71,1,344373768,349156737,157306536,41334300,6980904,785862,58968,2844,80,1
%N A380860 Triangle read by rows: T(n,m) (0<=m<=n) = number of positive n-digit numbers that have exactly m copies of a specific, previously selected positive base-10 digit among its digits.
%H A380860 Paolo Xausa, <a href="/A380860/b380860.txt">Table of n, a(n) for n = 0..11475</a> (rows 0..150 of triangle, flattened).
%F A380860 T(n,m) = floor(9^(n-m)*(binomial(n-1,m-1)+8/9*binomial(n-1,m))), considering binomial(k,-1)=0 for k>=0 and binomial(k,l)=0 for k>=0 with k<l.
%e A380860 Rows n=0..7 of the triangle are:
%e A380860         1;
%e A380860         8,       1;
%e A380860        72,      17,       1;
%e A380860       648,     225,      26,      1;
%e A380860      5832,    2673,     459,     35,     1;
%e A380860     52488,   29889,    6804,    774,    44,    1;
%e A380860    472392,  321489,   91125,  13770,  1170,   53,  1;
%e A380860   4251528, 3365793, 1141614, 215055, 24300, 1647, 62, 1;
%e A380860   ...
%p A380860 seq(lprint(seq(floor(9^(n-m)*(binomial(n-1, m-1)+(8/9)*binomial(n-1, m))), m=0..n)), n=0..7);
%t A380860 A380860[n_, m_] := Floor[9^(n-m)*(Binomial[n-1, m-1] + 8/9*Binomial[n-1, m])];
%t A380860 Table[A380860[n, m], {n, 0, 10}, {m, 0, n}] (* _Paolo Xausa_, Feb 07 2025 *)
%Y A380860 Row sums give A052268 (for n>=1).
%Y A380860 Columns k=0-1 give: A055275, A081044(n-1) (for n>=1).
%K A380860 nonn,base,tabl
%O A380860 0,2
%A A380860 _Peter Starek_, Feb 06 2025