A174693 Triangle read by rows: T(n,k) = n! * binomial(n, k) * Eulerian(n + 1, k) - n! + 1.

1, 1, 1, 1, 15, 1, 1, 193, 193, 1, 1, 2473, 9481, 2473, 1, 1, 34081, 362281, 362281, 34081, 1, 1, 517681, 12862081, 34789681, 12862081, 517681, 1, 1, 8709121, 454366081, 2755186561, 2755186561, 454366081, 8709121, 1, 1, 161884801, 16491807361, 199225272961

Offset

0,5

Comments

Triangle is symmetrical.

Links

Table of n, a(n) for n=0..39.

Example

Triangle begins:
  {1},
  {1, 1},
  {1, 15, 1},
  {1, 193, 193, 1},
  {1, 2473, 9481, 2473, 1},
  {1, 34081, 362281, 362281, 34081, 1},
  {1, 517681, 12862081, 34789681, 12862081, 517681, 1},
  ...

Mathematica

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

Crossrefs

Cf. A173018.

Sequence in context: A155493 A156939 A174187 * A340430 A022178 A176639

Adjacent sequences: A174690 A174691 A174692 * A174694 A174695 A174696

Keyword

nonn,tabl,less

Author

Roger L. Bagula, Mar 27 2010

Extensions

Edited by Sean A. Irvine, Mar 10 2026

Status

approved