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A129455 An analog of Pascal's triangle based on A129454. T(n,k)= A129454(n)/(A129454(n-k)*A129454(k)). 3

%I

%S 1,1,1,1,2,1,1,3,3,1,1,256,384,256,1,1,5,640,640,5,1,1,1146617856,

%T 2866544640,244611809280,2866544640,1146617856,1,1,7,4013162496,

%U 6688604160,6688604160,4013162496,7,1,1,35184372088832,123145302310912

%N An analog of Pascal's triangle based on A129454. T(n,k)= A129454(n)/(A129454(n-k)*A129454(k)).

%C It appears that the T(n,k) are always integers. This would follow from the conjectured prime factorization given in A129454. Calculation suggests that the binomial coefficients C(n,k) divide T(n,k) and that T(n,k)/C(n,k) are perfect sixth powers.

%F T(n,k) = product_{h=1..n}product_{i=1..n}product_{j=1..n} gcd(h,i,j)/(product_{h=1..n-k}product_{i=1..n-k}product_{j=1..n-k} gcd(h,i,j)*product_{h=1..k}product_{i=1..k}product_{j=1..k} gcd(h,i,j)).

%e Triangle starts:

%e 1

%e 1 1

%e 1 2 1

%e 1 3 3 1

%e 1 256 384 256 1

%Y Cf. A007318, A092287, A129453, A129454.

%K nonn,tabl

%O 0,5

%A _Peter Bala_, Apr 16 2007

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Last modified July 26 01:49 EDT 2021. Contains 346294 sequences. (Running on oeis4.)