A172342
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=5.
Original entry on oeis.org
1, 1, 1, 1, 5, 1, 1, 26, 26, 1, 1, 135, 702, 135, 1, 1, 701, 18927, 18927, 701, 1, 1, 3640, 510328, 2649780, 510328, 3640, 1, 1, 18901, 13759928, 370988828, 370988828, 13759928, 18901, 1, 1, 98145, 371007729, 51941082060, 269708877956
Offset: 0
1;
1, 1;
1, 5, 1;
1, 26, 26, 1;
1, 135, 702, 135, 1;
1, 701, 18927, 18927, 701, 1;
1, 3640, 510328, 2649780, 510328, 3640, 1;
1, 18901, 13759928, 370988828, 370988828, 13759928, 18901, 1;
1, 98145, 371007729, 51941082060, 269708877956, 51941082060, 371007729, 98145, 1;
-
Clear[f, c, a, t];
f[0, a_] := 0; f[1, a_] := 1;
f[n_, a_] := f[n, a] = a*f[n - 1, 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}]
A172345
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=7.
Original entry on oeis.org
1, 1, 1, 1, 7, 1, 1, 50, 50, 1, 1, 357, 2550, 357, 1, 1, 2549, 129999, 129999, 2549, 1, 1, 18200, 6627400, 47319636, 6627400, 18200, 1, 1, 129949, 337867400, 17224480052, 17224480052, 337867400, 129949, 1, 1, 927843, 17224610001, 6269758040364
Offset: 0
1;
1, 1;
1, 7, 1;
1, 50, 50, 1;
1, 357, 2550, 357, 1;
1, 2549, 129999, 129999, 2549, 1;
1, 18200, 6627400, 47319636, 6627400, 18200, 1;
1, 129949, 337867400, 17224480052, 17224480052, 337867400, 129949, 1;
1, 927843, 17224610001, 6269758040364, 44766423655148, 6269758040364, 17224610001, 927843, 1;
-
Clear[f, c, a, t];
f[0, a_] := 0; f[1, a_] := 1;
f[n_, a_] := f[n, a] = a*f[n - 1, 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}]
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