A176161 Triangle read by rows: T(n,k) = (1 + Eulerian(n+1, k))^n.

1, 2, 2, 4, 25, 4, 8, 1728, 1728, 8, 16, 531441, 20151121, 531441, 16, 32, 656356768, 2553954421743, 2553954421743, 656356768, 32, 64, 3138428376721, 2868517689517932544, 199370042958924478369, 2868517689517932544, 3138428376721, 64

Offset

0,2

Links

Table of n, a(n) for n=0..27.

Example

Triangle begins:
  {1},
  {2, 2},
  {4, 25, 4},
  {8, 1728, 1728, 8},
  {16, 531441, 20151121, 531441, 16},
  {32, 656356768, 2553954421743, 2553954421743, 656356768, 32},
  ...

Mathematica

Clear[p, n, m];
<< DiscreteMath`Combinatorica`
p[x_, n_, m_] := (1 + Eulerian[n+1, m]*x)^n;
Table[Table[ Apply[Plus, CoefficientList[p[x, n, m], x]], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Cf. A173018.

Sequence in context: A307969 A212672 A362766 * A006829 A154594 A098335

Adjacent sequences: A176158 A176159 A176160 * A176162 A176163 A176164

Keyword

nonn,tabl,less

Author

Roger L. Bagula, Apr 10 2010

Extensions

Edited by Sean A. Irvine, Mar 22 2026

Status

approved