A174730 Triangle read by rows: T(n,k) = (1-4^n) * Eulerian(n + 1, m) + 4^n.

1, 1, 1, 1, -44, 1, 1, -629, -629, 1, 1, -6374, -16574, -6374, 1, 1, -57287, -307922, -307922, -57287, 1, 1, -487304, -4873049, -9889424, -4873049, -487304, 1, 1, -4030217, -70315835, -255869693, -255869693, -70315835, -4030217, 1, 1, -32833034, -957269744, -5782349654, -10235846114, -5782349654, -957269744, -32833034, 1

Offset

0,5

Comments

Triangle is symmetric.

Links

Table of n, a(n) for n=0..44.

Example

Triangle begins:
  {1},
  {1, 1},
  {1, -44, 1},
  {1, -629, -629, 1},
  {1, -6374, -16574, -6374, 1},
  {1, -57287, -307922, -307922, -57287, 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, A174729.

Sequence in context: A350718 A022075 A178986 * A037939 A040010 A169857

Adjacent sequences: A174727 A174728 A174729 * A174731 A174732 A174733

Keyword

sign,tabl,less

Author

Roger L. Bagula, Mar 28 2010

Extensions

Edited by Sean A. Irvine, Mar 12 2026

Status

approved