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1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 256, 384, 256, 1, 1, 5, 640, 640, 5, 1, 1, 1146617856, 2866544640, 244611809280, 2866544640, 1146617856, 1, 1, 7, 4013162496, 6688604160, 6688604160, 4013162496, 7, 1, 1, 35184372088832, 123145302310912, 47066867504069920948224, 919274755938865643520, 47066867504069920948224, 123145302310912, 35184372088832, 1
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OFFSET
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0,5
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COMMENTS
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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.
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LINKS
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FORMULA
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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)) ).
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EXAMPLE
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Triangle starts:
1;
1, 1;
1, 2, 1;
1, 3, 3, 1;
1, 256, 384, 256, 1;
1, 5, 640, 640, 5, 1;
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MATHEMATICA
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A129454[n_]:= Product[GCD[j, k, m], {j, n-1}, {k, n-1}, {m, n-1}];
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PROG
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(Magma)
A129454:= func< n | n le 1 select 1 else (&*[(&*[(&*[GCD(GCD(j, k), m): k in [1..n-1]]): j in [1..n-1]]): m in [1..n-1]]) >;
(SageMath)
def A129454(n): return product(product(product(gcd(gcd(j, k), m) for k in range(1, n)) for j in range(1, n)) for m in range(1, n))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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