A176160 A polynomial coefficient sequence:p(x,n,m)=(1 + 4*Binomial[n, m]*x)^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

Offset

0,2

Comments

Row sums are:

{1, 10, 131, 4644, 558917, 239886854, 385958597703, 2280119446470280, 52063212260725437065, 4384388899674032467912458, 1449048908960986942519336016459,...}.

Links

Table of n, a(n) for n=0..29.

Formula

p(x,n,m)=(1 + 4*Binomial[n, m]*x)^n

Example

{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},
{390625, 1406408618241, 26584441929064321, 6568408355712890625, 38873223852623509441, 6568408355712890625, 26584441929064321, 1406408618241, 390625},
{1953125, 129961739795077, 28334269484119140625, 56062067225927988301777, 2136104048211642384765625, 2136104048211642384765625, 56062067225927988301777, 28334269484119140625, 129961739795077, 1953125},
{9765625, 13422659310152401, 37738596846955704499801, 662904189510194816788612801, 176994576151109753197786640401, 1093733872802526507260136674401, 176994576151109753197786640401, 662904189510194816788612801, 37738596846955704499801, 13422659310152401, 9765625}

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

Sequence in context: A189318 A257615 A257624 * A222281 A214706 A203191

Adjacent sequences: A176157 A176158 A176159 * A176161 A176162 A176163

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Apr 10 2010

Status

approved