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

0,8

Comments

Start from the generalized Fibonacci sequence A015441 and its partial products c(n) = 1, 1, 1, 7, 91, 5005, 665665, 308202895, 388643850595, 1569732512553205... Then t(n,k) = c(n)/(c(k)*c(n-k)).

Row sums are 1, 2, 3, 16, 119, 1542, 28483, 1091756, 70288239, 7576979362, 1345651717403,..

Links

Table of n, a(n) for n=0..48.

Example

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;

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}]

Crossrefs

Cf. A010048 (m=1), A015109 (m=2), A172350 (m=5), A172352 (m=7).

Sequence in context: A278657 A242914 A046542 * A140136 A281123 A171707

Adjacent sequences: A172348 A172349 A172350 * A172352 A172353 A172354

Keyword

nonn,tabl

Author

Roger L. Bagula and Gary W. Adamson, Feb 01 2010

Status

approved