login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A172343 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. 2
1, 1, 1, 1, 6, 1, 1, 37, 37, 1, 1, 228, 1406, 228, 1, 1, 1405, 53390, 53390, 1405, 1, 1, 8658, 2027415, 12493260, 2027415, 8658, 1, 1, 53353, 76988379, 2923477635, 2923477635, 76988379, 53353, 1, 1, 328776, 2923530988, 684106251192 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Start from the generalized Fibonacci sequence A005668 and its partial products c(n) = 1, 1, 6, 222, 50616, 71115480, 615717825840, 32850393162041520... Then t(n,k) = c(n)/(c(k)*c(n-k)).

Row sums are 1, 2, 8, 76, 1864, 109592, 16565408, 6001038736, 5589714971584,

12478331908166432, 71624411004755875328,...

LINKS

Table of n, a(n) for n=0..39.

EXAMPLE

1;

1, 1;

1, 6, 1;

1, 37, 37, 1;

1, 228, 1406, 228, 1;

1, 1405, 53390, 53390, 1405, 1;

1, 8658, 2027415, 12493260, 2027415, 8658, 1;

1, 53353, 76988379, 2923477635, 2923477635, 76988379, 53353, 1;

1, 328776, 2923530988, 684106251192, 4215654749670, 684106251192, 2923530988, 328776, 1;

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}]

CROSSREFS

Cf. A010048 (m=1), A099927 (m=2), A172342 (m=5), A172345 (m=7).

Sequence in context: A178232 A203338 A158116 * A058875 A156764 A156765

Adjacent sequences:  A172340 A172341 A172342 * A172344 A172345 A172346

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Feb 01 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 15 20:11 EDT 2019. Contains 327086 sequences. (Running on oeis4.)