A174692 Triangle read by rows: T(n,k) = n! * Eulerian(n + 1, k)^2 - k! + 1.

1, 1, 1, 1, 31, 1, 1, 721, 721, 1, 1, 16201, 104521, 16201, 1, 1, 389761, 10944361, 10944361, 389761, 1, 1, 10367281, 1021305601, 4202679601, 1021305601, 10367281, 1, 1, 307480321, 92886433921, 1229523926401, 1229523926401, 92886433921, 307480321, 1

Offset

0,5

Comments

Triangle is symmetric.

Links

Table of n, a(n) for n=0..35.

Example

Triangle begins:
  {1},
  {1, 1},
  {1, 31, 1},
  {1, 721, 721, 1},
  {1, 16201, 104521, 16201, 1},
  {1, 389761, 10944361, 10944361, 389761, 1},
  {1, 10367281, 1021305601, 4202679601, 1021305601, 10367281, 1},
  ...

Mathematica

<< DiscreteMath`Combinatorica`
t[n_, m_] = n!*Eulerian[n + 1, m]^2 - n! + 1;
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Cf. A173018.

Sequence in context: A040961 A300656 A239633 * A172302 A103474 A047687

Adjacent sequences: A174689 A174690 A174691 * A174693 A174694 A174695

Keyword

nonn,tabl,less

Author

Roger L. Bagula, Mar 27 2010

Extensions

Edited by Sean A. Irvine, Mar 09 2026

Status

approved