A174411 Triangle read by rows: T(n,k) = c(n) / c(max(k, n-k)) where c(n) = Product_{i=1..n} F(i)*F(i+1) and F(i) the Fibonacci numbers.

1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 15, 90, 15, 1, 1, 40, 600, 600, 40, 1, 1, 104, 4160, 62400, 4160, 104, 1, 1, 273, 28392, 1135680, 1135680, 28392, 273, 1, 1, 714, 194922, 20271888, 810875520, 20271888, 194922, 714, 1, 1, 1870, 1335180, 364504140

Offset

0,5

Links

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

Example

Triangle begins:
  {1},
  {1, 1},
  {1, 2, 1},
  {1, 6, 6, 1},
  {1, 15, 90, 15, 1},
  {1, 40, 600, 600, 40, 1},
  {1, 104, 4160, 62400, 4160, 104, 1},
  {1, 273, 28392, 1135680, 1135680, 28392, 273, 1},
  ...

Mathematica

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]*f[i + 1, a], {i, 1, n}]];
t[n_, m_, q_] = If[Floor[n/2] >= m, c[n, q]/c[n - m, q], c[n, q]/c[m, q]];
Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 1, 10}]

Crossrefs

Cf. A000045.

Sequence in context: A385626 A329228 A172373 * A322620 A376935 A155795

Adjacent sequences: A174408 A174409 A174410 * A174412 A174413 A174414

Keyword

nonn,tabl,less

Author

Roger L. Bagula, Mar 19 2010

Extensions

Edited by Sean A. Irvine, Mar 02 2026

Status

approved