A173887 Fibonacci triple product triangle:c(n)=If[n == 0, 1, Product[Fibonacci[(i - 1)]*Fibonacci[i]*Fibonacci[i + 1], {i, 2, n}];t(n,m)=c(n)/(c(m)*c(n-m))

1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 30, 90, 30, 1, 1, 120, 1800, 1800, 120, 1, 1, 520, 31200, 156000, 31200, 520, 1, 1, 2184, 567840, 11356800, 11356800, 567840, 2184, 1, 1, 9282, 10135944, 878448480, 3513793920, 878448480, 10135944, 9282, 1, 1, 39270

Offset

0,5

Comments

Row sums are:

{1, 2, 4, 14, 152, 3842, 219442, 23853650, 5290981334, 2432822210282,

2340979254062902,...}.

Links

Table of n, a(n) for n=0..46.

Formula

c(n)=If[n == 0, 1, Product[Fibonacci[(i - 1)]*Fibonacci[i]*Fibonacci[i + 1], {i, 2, n}];

t(n,m)=c(n)/(c(m)*c(n-m))

Example

{1},
{1, 1},
{1, 2, 1},
{1, 6, 6, 1},
{1, 30, 90, 30, 1},
{1, 120, 1800, 1800, 120, 1},
{1, 520, 31200, 156000, 31200, 520, 1},
{1, 2184, 567840, 11356800, 11356800, 567840, 2184, 1},
{1, 9282, 10135944, 878448480, 3513793920, 878448480, 10135944, 9282, 1},
{1, 39270, 182252070, 66339753480, 1149889060320, 1149889060320, 66339753480, 182252070, 39270, 1},
{1, 166430, 3267853050, 5055368668350, 368030839055880, 1594800302575480, 368030839055880, 5055368668350, 3267853050, 166430, 1}

Mathematica

c[n_] = If[n == 0, 1, Product[Fibonacci[(i - 1)]*Fibonacci[i]*Fibonacci[i + 1], {i, 2, n}];
t[n_, m_] = c[n]/(c[m]*c[n - m]);
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A009963 A008300 A321789 * A288025 A137376 A039761

Adjacent sequences: A173884 A173885 A173886 * A173888 A173889 A173890

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 01 2010

Status

approved