A176159 Triangle T(n,m) = (1 + binomial(n, m))^n, n>=0, 0<=m<=n.

1, 2, 2, 4, 9, 4, 8, 64, 64, 8, 16, 625, 2401, 625, 16, 32, 7776, 161051, 161051, 7776, 32, 64, 117649, 16777216, 85766121, 16777216, 117649, 64, 128, 2097152, 2494357888, 78364164096, 78364164096, 2494357888, 2097152, 128, 256, 43046721, 500246412961, 111429157112001, 645753531245761, 111429157112001, 500246412961, 43046721, 256

Offset

0,2

Comments

Row sums are:1, 4, 17, 144, 3683, 337718, 119555979, 161721238528, 869612424389639, 17653003315264793202, 1425670580988729857215055,....

The entry T(n,m) is also the sum of the coefficients of the polynomial (1+binomial(n,m)*x)^n.

Links

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

Example

Triangle begins:
  {1},
  {2, 2},
  {4, 9, 4},
  {8, 64, 64, 8},
  {16, 625, 2401, 625, 16},
  {32, 7776, 161051, 161051, 7776, 32},
  {64, 117649, 16777216, 85766121, 16777216, 117649, 64},
  {128, 2097152, 2494357888, 78364164096, 78364164096, 2494357888, 2097152, 128},
  {256, 43046721, 500246412961, 111429157112001, 645753531245761, 111429157112001, 500246412961, 43046721, 256},
  ..

Mathematica

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

Crossrefs

Sequence in context: A021982 A165251 A264128 * A280859 A280961 A280362

Adjacent sequences: A176156 A176157 A176158 * A176160 A176161 A176162

Keyword

nonn,tabl

Author

Roger L. Bagula, Apr 10 2010

Status

approved