A176159 A polynomial coefficient sequence:p(x,n,m)=(1 + Binomial[n, m]*x)^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

Offset

0,2

Comments

Row sums are:

{1, 4, 17, 144, 3683, 337718, 119555979, 161721238528, 869612424389639,

17653003315264793202, 1425670580988729857215055,...}.

Links

Table of n, a(n) for n=0..37.

Formula

p(x,n,m)=(1 + Binomial[n, m]*x)^n

Example

{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},
{512, 1000000000, 129961739795077, 231616946283203125, 8594754748609397887, 8594754748609397887, 231616946283203125, 129961739795077, 1000000000, 512},
{1024, 25937424601, 42420747482776576, 672749994932560009201, 174913992535407978606601, 1074497011086501939579049, 174913992535407978606601, 672749994932560009201, 42420747482776576, 25937424601, 1024}

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,uned

Author

Roger L. Bagula, Apr 10 2010

Status

approved