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A176159 A polynomial coefficient sequence:p(x,n,m)=(1 + Binomial[n, m]*x)^n 0
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 5 15:06 EST 2021. Contains 349557 sequences. (Running on oeis4.)