A173886 Fibonacci double product triangle:If[n == 1, 1, If[n == 0, 1, Product[Fibonacci[(i - 1)]*Fibonacci[i], {i, 2, n}]]];t(n,m)=c(n)/(c(m)*c(n-m))

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 6, 12, 6, 1, 1, 15, 90, 90, 15, 1, 1, 40, 600, 1800, 600, 40, 1, 1, 104, 4160, 31200, 31200, 4160, 104, 1, 1, 273, 28392, 567840, 1419600, 567840, 28392, 273, 1, 1, 714, 194922, 10135944, 67572960, 67572960, 10135944, 194922

Offset

0,8

Comments

Row sums are:

{1, 2, 3, 6, 26, 212, 3082, 70930, 2612612, 155809082, 15109345682,...}.

Links

Table of n, a(n) for n=0..52.

Formula

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

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

Example

{1},
{1, 1},
{1, 1, 1},
{1, 2, 2, 1},
{1, 6, 12, 6, 1},
{1, 15, 90, 90, 15, 1},
{1, 40, 600, 1800, 600, 40, 1},
{1, 104, 4160, 31200, 31200, 4160, 104, 1},
{1, 273, 28392, 567840, 1419600, 567840, 28392, 273, 1},
{1, 714, 194922, 10135944, 67572960, 67572960, 10135944, 194922, 714, 1},
{1, 1870, 1335180, 182252070, 3159035880, 8424095680, 3159035880, 182252070, 1335180, 1870, 1}

Mathematica

c[n_] = If[n == 1, 1, If[n == 0, 1, Product[Fibonacci[(i - 1)]*Fibonacci[i], {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: A174640 A138169 A139331 * A090441 A340591 A155794

Adjacent sequences: A173883 A173884 A173885 * A173887 A173888 A173889

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 01 2010

Status

approved