A174729 Triangle read by rows: T(n,k) = (1-3^n) * Eulerian(n + 1, k) + 3^n.

1, 1, 1, 1, -23, 1, 1, -259, -259, 1, 1, -1999, -5199, -1999, 1, 1, -13551, -72841, -72841, -13551, 1, 1, -86631, -866319, -1758119, -866319, -86631, 1, 1, -537755, -9382311, -34140947, -34140947, -9382311, -537755, 1, 1, -3286559, -95821919

Offset

0,5

Comments

Triangle is symmetrical.

Links

Table of n, a(n) for n=0..38.

Example

Triangle begins:
  {1},
  {1, 1},
  {1, -23, 1},
  {1, -259, -259, 1},
  {1, -1999, -5199, -1999, 1},
  {1, -13551, -72841, -72841, -13551, 1},
  {1, -86631, -866319, -1758119, -866319, -86631, 1},
  ...

Mathematica

<< DiscreteMath`Combinatorica`
t[n_, m_, q_] = (1 - q^n)*Eulerian[n + 1, m] - (1 - q^n) + 1;
Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}]

Crossrefs

Cf. A173018.

Sequence in context: A040529 A234788 A144445 * A022186 A015151 A040539

Adjacent sequences: A174726 A174727 A174728 * A174730 A174731 A174732

Keyword

sign,tabl,less

Author

Roger L. Bagula, Mar 28 2010

Extensions

Edited by Sean A. Irvine, Mar 11 2026

Status

approved