A174036 Triangle read by rows: T(n,k) = 1 if k=0 or k=n, otherwise T(n,k) = binomial(Eulerian(n+1, k), min(n-k,k)).

1, 1, 1, 1, 4, 1, 1, 11, 11, 1, 1, 26, 2145, 26, 1, 1, 57, 45451, 45451, 57, 1, 1, 120, 708645, 2347470160, 708645, 120, 1, 1, 247, 9212778, 634928765569, 634928765569, 9212778, 247, 1, 1, 502, 106689528, 114483233476184, 24796191085864033165

Offset

0,5

Links

Table of n, a(n) for n=0..40.

Example

Triangle begins:
  {1},
  {1, 1},
  {1, 4, 1},
  {1, 11, 11, 1},
  {1, 26, 2145, 26, 1},
  {1, 57, 45451, 45451, 57, 1},
  {1, 120, 708645, 2347470160, 708645, 120, 1},
  ...

Mathematica

<< DiscreteMath`Combinatorica`
Table[Table[If[m == 0 || m == n, 1, Binomial[Eulerian[n + 1, m], If[Floor[n/2] < m, n - m, m]]], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Cf. A173018, A174035.

Sequence in context: A285357 A174526 A008292 * A157221 A146967 A173152

Adjacent sequences: A174033 A174034 A174035 * A174037 A174038 A174039

Keyword

nonn,tabl,less

Author

Roger L. Bagula, Mar 06 2010

Status

approved