A172346 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=8.

1, 1, 1, 1, 8, 1, 1, 65, 65, 1, 1, 528, 4290, 528, 1, 1, 4289, 283074, 283074, 4289, 1, 1, 34840, 18678595, 151727664, 18678595, 34840, 1, 1, 283009, 1232504195, 81326315267, 81326315267, 1232504195, 283009, 1, 1, 2298912, 81326598276

Offset: 0

Author

Roger L. Bagula, Feb 01 2010

Keywords

• nonn
• tabl

Comments

Start from the generalized Fibonacci sequence A041025 and its partial products c(n) = 1, 1, 8, 520, 274560, 1177587840, 41027160345600,... Then t(n,k) = c(n)/(c(k)*c(n-k)).

Row sums are 1, 2, 10, 132, 5348, 574728, 189154536, 165118204944, 441439547818768, 3130197658239760416, 67978275921898969849504,...

Examples

			1;
1, 1;
1, 8, 1;
1, 65, 65, 1;
1, 528, 4290, 528, 1;
1, 4289, 283074, 283074, 4289, 1;
1, 34840, 18678595, 151727664, 18678595, 34840, 1;
1, 283009, 1232504195, 81326315267, 81326315267, 1232504195, 283009, 1;
1, 2298912, 81326598276, 43591056675936, 354094776672518, 43591056675936, 81326598276, 2298912, 1;
		

Crossrefs

Cf. A010048 (m=1), A099927 (m=2), A172345 (m=7).

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}]