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A292879 Triangle read by rows: T(n,k) (n>=1, 4<=k<=n+3) is the number of k-sequences of balls colored with at most n colors such that exactly three balls are of a color seen previously in the sequence.

%I A292879 #9 Sep 28 2017 08:47:33
%S A292879 1,2,30,3,90,540,4,180,2160,8400,5,300,5400,42000,126000,6,450,10800,
%T A292879 126000,756000,1905120,7,630,18900,294000,2646000,13335840,29635200,8,
%U A292879 840,30240,588000,7056000,53343360,237081600,479001600,9,1080,45360,1058400,15876000,160030080,1066867200,4311014400,8083152000
%N A292879 Triangle read by rows: T(n,k) (n>=1, 4<=k<=n+3) is the number of k-sequences of balls colored with at most n colors such that exactly three balls are of a color seen previously in the sequence.
%F A292879 [binomial(k,4)+10*binomial(k,5)+15*binomial(k,6)]*n!/(n+3-k)!
%e A292879   n=1 => AAAA -> T(1,4)=1
%e A292879   n=2 => AAAA,BBBB -> T(2,4)=2
%e A292879          AAAAB,AAABA,AABAA,ABAAA,BAAAA,BBBBA,BBBAB,BBABB,BABBB,ABBBB,
%e A292879          AAABB,AABAB,AABBA,ABAAB,ABABA,ABBAA,BAAAB,BAABA,BABAA,BBAAA,
%e A292879          BBBAA,BBABA,BBAAB,BABBA,BABAB,BAABB,ABBBA,ABBAB,ABABB,AABBB -> T(2,5)=30
%e A292879 Triangle begins:
%e A292879 1;
%e A292879 2,   30;
%e A292879 3,   90,   540;
%e A292879 4,  180,  2160,    8400;
%e A292879 5,  300,  5400,   42000,   126000;
%e A292879 6,  450, 10800,  126000,   756000,   1905120;
%e A292879 7,  630, 18900,  294000,  2646000,  13335840,   29635200;
%e A292879 8,  840, 30240,  588000,  7056000,  53343360,  237081600,  479001600;
%e A292879 ...
%Y A292879 Main diagonal is A037961.
%K A292879 nonn,tabl
%O A292879 1,2
%A A292879 _Jeremy Dover_, Sep 25 2017