A385850 Triangle read by rows: T(n,k) = denominator((Sum_{i=1..k} (n-i+1)^2)/(Sum_{i=1..k} i^2)), with 1 <= k <= n.
1, 1, 1, 1, 5, 1, 1, 1, 14, 1, 1, 5, 7, 5, 1, 1, 5, 2, 15, 11, 1, 1, 1, 7, 5, 11, 91, 1, 1, 5, 14, 5, 11, 91, 20, 1, 1, 1, 7, 3, 11, 91, 1, 51, 1, 1, 5, 2, 5, 1, 91, 20, 51, 95, 1, 1, 5, 7, 5, 11, 91, 5, 17, 95, 77, 1, 1, 1, 14, 15, 11, 7, 4, 51, 95, 77, 46, 1
Offset: 1
Examples
Triangle of the fractions begins as: 1/1; 4/1, 1/1; 9/1, 13/5, 1/1; 16/1, 5/1, 29/14, 1/1; 25/1, 41/5, 25/7, 9/5, 1/1; 36/1, 61/5, 11/2, 43/15, 18/11, 1/1; 49/1, 17/1, 55/7, 21/5, 27/11, 139/91, 1/1; ... A385849(4,3)/T(4,3) = (4^2 + 3^2 + 2^2)/(1^2 + 2^2 + 3^2) = 29/14.
Links
- Stefano Spezia, Table of n, a(n) for n = 1..11325 (first 150 rows of the triangle, flattened)
Programs
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Mathematica
T[n_,k_]:=Denominator[(1-3k+2k^2+6n-6k*n+6n^2)/(1+3k+2k^2)]; Table[T[n,k],{n,12},{k,n}]//Flatten
Formula
T(n,k) = denominator((1 - 3*k + 2*k^2 + 6*n - 6*k*n + 6*n^2)/(1 + 3*k + 2*k^2)).