A174545 Triangle read by rows: T(n,0) = T(n,n) = 1, T(n,k) = Stirling2(n,m) * 2^m where m = min(k,n-k).

1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 28, 2, 1, 1, 2, 60, 60, 2, 1, 1, 2, 124, 720, 124, 2, 1, 1, 2, 252, 2408, 2408, 252, 2, 1, 1, 2, 508, 7728, 27216, 7728, 508, 2, 1, 1, 2, 1020, 24200, 124320, 124320, 24200, 1020, 2, 1, 1, 2, 2044, 74640, 545680, 1360800, 545680, 74640, 2044, 2, 1

Offset

0,5

Links

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

Example

Triangle begins:
  {1},
  {1, 1},
  {1, 2, 1},
  {1, 2, 2, 1},
  {1, 2, 28, 2, 1},
  {1, 2, 60, 60, 2, 1},
  {1, 2, 124, 720, 124, 2, 1},
  {1, 2, 252, 2408, 2408, 252, 2, 1},
  ...

Maple

T:= (n, k)-> `if`(k=0 or k=n, 1, (m-> Stirling2(n, m)*2^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. A174546.

Sequence in context: A152719 A107044 A141591 * A102523 A379130 A323023

Adjacent sequences: A174542 A174543 A174544 * A174546 A174547 A174548

Keyword

nonn,tabl

Author

Roger L. Bagula, Mar 22 2010

Extensions

Edited by Sean A. Irvine, Mar 03 2026

Status

approved