A176160 Triangle read by rows: T(n,k) = (1 + 4*binomial(n, k))^n.

1, 5, 5, 25, 81, 25, 125, 2197, 2197, 125, 625, 83521, 390625, 83521, 625, 3125, 4084101, 115856201, 115856201, 4084101, 3125, 15625, 244140625, 51520374361, 282429536481, 51520374361, 244140625, 15625, 78125, 17249876309, 32057708828125, 1107984764452581, 1107984764452581, 32057708828125, 17249876309, 78125

Offset

0,2

Links

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

Example

Triangle begins:
  {1},
  {5, 5},
  {25, 81, 25},
  {125, 2197, 2197, 125},
  {625, 83521, 390625, 83521, 625},
  {3125, 4084101, 115856201, 115856201, 4084101, 3125},
  ...

Mathematica

Clear[p, n, m];
p[x_, n_, m_] := (1 + 4*Binomial[n, m]*x)^n;
Table[Table[ Apply[Plus, CoefficientList[p[x, n, m], x]], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Cf. A000351 (column k=0 and main diagonal).

Sequence in context: A189318 A257615 A257624 * A222281 A214706 A203191

Adjacent sequences: A176157 A176158 A176159 * A176161 A176162 A176163

Keyword

nonn,tabl,less

Author

Roger L. Bagula, Apr 10 2010

Extensions

Edited by Sean A. Irvine, Mar 19 2026

Status

approved