A172350 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, 1, 1, 1, 6, 6, 1, 1, 11, 66, 11, 1, 1, 41, 451, 451, 41, 1, 1, 96, 3936, 7216, 3936, 96, 1, 1, 301, 28896, 197456, 197456, 28896, 301, 1, 1, 781, 235081, 3761296, 14019376, 3761296, 235081, 781, 1, 1, 2286, 1785366, 89565861, 781665696

Offset

0,8

Comments

Start from the generalized Fibonacci sequence A015440 and its partial products c(n) = 1, 1, 1, 6, 66, 2706, 259776, 78192576, 61068401856, 139602366642816... Then t(n,k) = c(n)/(c(k)*c(n-k)).

Row sums are 1, 2, 3, 14, 90, 986, 15282, 453308, 22013694, 1746038420, 222562828116,...

Links

Table of n, a(n) for n=0..49.

Example

1;
1, 1;
1, 1, 1;
1, 6, 6, 1;
1, 11, 66, 11, 1;
1, 41, 451, 451, 41, 1;
1, 96, 3936, 7216, 3936, 96, 1;
1, 301, 28896, 197456, 197456, 28896, 301, 1;
1, 781, 235081, 3761296, 14019376, 3761296, 235081, 781, 1;
1, 2286, 1785366, 89565861, 781665696, 781665696, 89565861, 1785366, 2286, 1;
1, 6191, 14152626, 1842200151, 50409295041, 118031520096, 50409295041, 1842200151, 14152626, 6191, 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), A172349 (m=4), A172351 (m=6).

Sequence in context: A021606 A341687 A046606 * A205457 A155868 A322622

Adjacent sequences: A172347 A172348 A172349 * A172351 A172352 A172353

Keyword

nonn,tabl

Author

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

Status

approved