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.

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

Author

Roger L. Bagula, Feb 01 2010

Keywords

• nonn
• tabl

Comments

Start from the generalized Fibonacci sequence A054413 and its partial products c(n) = 1, 1, 7, 350, 124950, 318497550, 5796655410000,... Then t(n,k) = c(n)/(c(k)*c(n-k)).

Row sums are 1, 2, 9, 102, 3266, 265098, 60610838, 35124954804, 57340390811566,

237262009585104396, 2765506241462282647452,...}

Examples

			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;
		

Crossrefs

Cf. A010048 (m=1), A099927 (m=2), A172343 (m=6), A172346 (m=8).

Programs

Mathematica

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}]