A385626 Table read by rows: T(n, k) = binomial(n, k) * fibonomial(n, k).

1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 12, 36, 12, 1, 1, 25, 150, 150, 25, 1, 1, 48, 600, 1200, 600, 48, 1, 1, 91, 2184, 9100, 9100, 2184, 91, 1, 1, 168, 7644, 61152, 127400, 61152, 7644, 168, 1, 1, 306, 25704, 389844, 1559376, 1559376, 389844, 25704, 306, 1

Offset

0,5

Links

Table of n, a(n) for n=0..54.

Formula

T(n, k) = A385630(n) / (A385630(n - k) * A385630(k)).

T(n, k) = A007318(n, k) * A010048(n, k).

Example

Table begins:
  [0] 1;
  [1] 1,   1;
  [2] 1,   2,     1;
  [3] 1,   6,     6,      1;
  [4] 1,  12,    36,     12,      1;
  [5] 1,  25,   150,    150,     25,        1;
  [6] 1,  48,   600,   1200,    600,       48,      1;
  [7] 1,  91,  2184,   9100,   9100,     2184,     91,     1;
  [8] 1, 168,  7644,  61152,  127400,   61152,   7644,   168,   1;
  [9] 1, 306, 25704, 389844, 1559376, 1559376, 389844, 25704, 306, 1;

Mathematica

FF[n_] := Factorial[n] Fibonorial[n]; T[n_, k_] := FF[n] / (FF[n-k] FF[k]);
Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten

Crossrefs

Cf. A385630, A003266, A007318, A010048.

Sequence in context: A145903 A223257 A173881 * A329228 A172373 A174411

Adjacent sequences: A385623 A385624 A385625 * A385627 A385628 A385629

Keyword

nonn,tabl

Author

Peter Luschny, Jul 05 2025

Status

approved