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.

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

Author

Roger L. Bagula, Feb 01 2010

Keywords

• nonn
• tabl
• easy

Comments

Start from the generalized Fibonacci sequence A052918 and its partial products c(n) = 1, 1, 5, 130, 17550, 12302550, 44781282000,... Then t(n,k) = c(n)/(c(k)*c(n-k)).

Row sums are 1, 2, 7, 54, 974, 39258, 3677718, 769535316, 374333253826, 406720191959532,...

Examples

			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;
		

Crossrefs

Cf. A010048 (m=1), A099927 (m=2), A172339 (m=3), A172343 (m=6).

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}]