A174546 Triangle read by rows: T(n,0) = T(n,n) = 1, T(n,k) = Stirling2(n,m) * 3^m where m = min(k,n-k).

1, 1, 1, 1, 3, 1, 1, 3, 3, 1, 1, 3, 63, 3, 1, 1, 3, 135, 135, 3, 1, 1, 3, 279, 2430, 279, 3, 1, 1, 3, 567, 8127, 8127, 567, 3, 1, 1, 3, 1143, 26082, 137781, 26082, 1143, 3, 1, 1, 3, 2295, 81675, 629370, 629370, 81675, 2295, 3, 1, 1, 3, 4599, 251910, 2762505, 10333575, 2762505, 251910, 4599, 3, 1

Offset

0,5

Links

Table of n, a(n) for n=0..65.

Example

Triangle begins:
  {1},
  {1, 1},
  {1, 3, 1},
  {1, 3, 3, 1},
  {1, 3, 63, 3, 1},
  {1, 3, 135, 135, 3, 1},
  {1, 3, 279, 2430, 279, 3, 1},
  {1, 3, 567, 8127, 8127, 567, 3, 1},
  ...

Maple

T:= (n, k)-> `if`(k=0 or k=n, 1, (m-> Stirling2(n, m)*3^m)(min(k, n-k))):
seq(seq(T(n, k), k=0..n), n=0..10);  # Alois P. Heinz, Mar 03 2026

Mathematica

t[n_, m_, q_] = If[m == 0 || m == n, 1, If[Floor[n/2] >= m, StirlingS2[n, m]*q^ m, StirlingS2[n, n - m]*q^(n - m)]];
Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 1, 10}]

Crossrefs

Cf. A174545.

Sequence in context: A143086 A327481 A152714 * A134444 A176149 A091442

Adjacent sequences: A174543 A174544 A174545 * A174547 A174548 A174549

Keyword

nonn,tabl

Author

Roger L. Bagula, Mar 22 2010

Status

approved