A172351 Triangle t(n,k) read by rows: fibonomial ratios c(n)/(c(k)*c(n-k)) where c are partial products of a generalized Fibonacci sequence with multiplier m=6.
1, 1, 1, 1, 1, 1, 1, 7, 7, 1, 1, 13, 91, 13, 1, 1, 55, 715, 715, 55, 1, 1, 133, 7315, 13585, 7315, 133, 1, 1, 463, 61579, 483835, 483835, 61579, 463, 1, 1, 1261, 583843, 11093017, 46931995, 11093017, 583843, 1261, 1, 1, 4039, 5093179, 336877411
Offset: 0
Examples
1; 1, 1; 1, 1, 1; 1, 7, 7, 1; 1, 13, 91, 13, 1; 1, 55, 715, 715, 55, 1; 1, 133, 7315, 13585, 7315, 133, 1; 1, 463, 61579, 483835, 483835, 61579, 463, 1; 1, 1261, 583843, 11093017, 46931995, 11093017, 583843, 1261, 1; 1, 4039, 5093179, 336877411, 3446515051, 3446515051, 336877411, 5093179, 4039, 1;
Programs
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Mathematica
Clear[f, c, a, t]; f[0, a_] := 0; f[1, a_] := 1; f[n_, a_] := f[n, a] = f[n - 1, a] + a*f[n - 2, a]; c[n_, a_] := If[n == 0, 1, Product[f[i, a], {i, 1, n}]]; t[n_, m_, a_] := c[n, a]/(c[m, a]*c[n - m, a]); Table[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}], {a, 1, 10}]; Table[Flatten[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}]], {a, 1, 10}]
Comments