A176158 A polynomial coefficient sequence:p(x,n,m)=(1 + 2*Binomial[n, m]*x)^n

1, 3, 3, 9, 25, 9, 27, 343, 343, 27, 81, 6561, 28561, 6561, 81, 243, 161051, 4084101, 4084101, 161051, 243, 729, 4826809, 887503681, 4750104241, 887503681, 4826809, 729, 2187, 170859375, 271818611107, 9095120158391, 9095120158391

Offset

0,2

Comments

Row sums are:

{1, 6, 43, 740, 41845, 8490790, 6534766679, 18734219262120,

209617607911694569, 8719076076193077820874, 1429879617351180068934959131,...}.

Links

Table of n, a(n) for n=0..32.

Formula

p(x,n,m)=(1 + 2*Binomial[n, m]*x)^n

Example

{1},
{3, 3},
{9, 25, 9},
{27, 343, 343, 27},
{81, 6561, 28561, 6561, 81},
{243, 161051, 4084101, 4084101, 161051, 243},
{729, 4826809, 887503681, 4750104241, 887503681, 4826809, 729},
{2187, 170859375, 271818611107, 9095120158391, 9095120158391, 271818611107, 170859375, 2187},
{6561, 6975757441, 111429157112001, 26584441929064321, 156225851787813921, 26584441929064321, 111429157112001, 6975757441, 6561},
{19683, 322687697779, 58871586708267913, 112455406951957393129, 4247023759235185531933, 4247023759235185531933, 112455406951957393129, 58871586708267913, 322687697779, 19683},
{59049, 16679880978201, 38941611811810745401, 660952768068482275874401, 174912544792453358346502201, 1078732544346879404306640625, 174912544792453358346502201, 660952768068482275874401, 38941611811810745401, 16679880978201, 59049}

Mathematica

Clear[p, n, m];
p[x_, n_, m_] := (1 + 2*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: A257180 A184694 A215885 * A083008 A268092 A229024

Adjacent sequences: A176155 A176156 A176157 * A176159 A176160 A176161

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Apr 10 2010

Status

approved