A176161 A polynomial coefficient sequence:p(x,n,m)=(1 + Eulerian[n+1, m]*x)^n

1, 2, 2, 4, 25, 4, 8, 1728, 1728, 8, 16, 531441, 20151121, 531441, 16, 32, 656356768, 2553954421743, 2553954421743, 656356768, 32, 64, 3138428376721, 2868517689517932544, 199370042958924478369, 2868517689517932544

Offset

0,2

Comments

Row sums are:

{1, 4, 33, 3472, 21214035, 5109221557086, 205107084614817097027,

453783529133254322918738275328, 361547381989668282146848252390995509407047,

22780472014232161482743233392389330388096130814042249050,

939396139967918712108082841030601737833778288529223531806669966647470647,...}.

Links

Table of n, a(n) for n=0..25.

Formula

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

Example

{1},
{2, 2},
{4, 25, 4},
{8, 1728, 1728, 8},
{16, 531441, 20151121, 531441, 16},
{32, 656356768, 2553954421743, 2553954421743, 656356768, 32},
{64, 3138428376721, 2868517689517932544, 199370042958924478369, 2868517689517932544, 3138428376721, 64},
{128, 57698133708111872, 26917472665460943581025664, 226864847093904002382080000000, 226864847093904002382080000000, 26917472665460943581025664, 57698133708111872, 128},
{256, 4097735106081111754561, 2074741111292483594610250857505921, 3673898216392037583173110761317250390625, 354199581407401984387339371435697070104321, 3673898216392037583173110761317250390625, 2074741111292483594610250857505921, 4097735106081111754561, 256},
{512, 1133291404818113212906550784, 1312811101347708143301620260114932495688161, 838996546850716044311879830367056713651935386463193, 11389397010567917214225957107087705112256185326232421875, 11389397010567917214225957107087705112256185326232421875, 838996546850716044311879830367056713651935386463193, 1312811101347708143301620260114932495688161, 1133291404818113212906550784, 512},
{1024, 1230014666706119434632766053957849, 6864780713384859620397143816163790449963622077236224, 2698415781762968480988828213779434219311563591181370644717489601, 7669181030746292525057997566387729666454040564886779550193375478515625, 924057772509594563518300322493400131698747451810582970574349149993070001, 7669181030746292525057997566387729666454040564886779550193375478515625, 2698415781762968480988828213779434219311563591181370644717489601, 6864780713384859620397143816163790449963622077236224, 1230014666706119434632766053957849, 1024}

Mathematica

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

Crossrefs

Sequence in context: A307969 A212672 A362766 * A006829 A154594 A098335

Adjacent sequences: A176158 A176159 A176160 * A176162 A176163 A176164

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Apr 10 2010

Status

approved