A174860 A triangle sequence of polynomial coefficients:p(x,n)=Sum[Eulerian[n+1, k]*(-x)^k*Sum[StirlingS2[n, m]*x^m, {m, 0, n - k}], {k, 0, n}]

1, 0, 1, 0, 1, -3, 0, 1, -8, -21, 0, 1, -19, -110, 281, 0, 1, -42, -528, 2813, 2508, 0, 1, -89, -2439, 23770, 25700, -105023, 0, 1, -184, -10967, 180843, 237505, -2253624, -439709, 0, 1, -375, -48180, 1283751, 2208948, -41164774, 4807292, 93525833, 0, 1

Offset

0,6

Comments

Row sums are:

{1, 1, -2, -28, 153, 4752, -58080, -2286135, 60612496, 2179207812,

-125325232468,...}.

Links

Table of n, a(n) for n=0..46.

Formula

p(x,n)=Sum[Eulerian[n+1, k]*(-x)^k*Sum[StirlingS2[n, m]*x^m, {m, 0, n - k}], {k, 0, n}];

t(n,m)=coefficients(p(x,n))

Example

{1},
{0, 1},
{0, 1, -3},
{0, 1, -8, -21},
{0, 1, -19, -110, 281},
{0, 1, -42, -528, 2813, 2508},
{0, 1, -89, -2439, 23770, 25700, -105023},
{0, 1, -184, -10967, 180843, 237505, -2253624, -439709},
{0, 1, -375, -48180, 1283751, 2208948, -41164774, 4807292, 93525833},
{0, 1, -758, -207450, 8687453, 22088335, -679447801, 423149836, 3295732928, -890794732},
{0, 1, -1525, -878429, 56832244, 238463701, -10478964222, 14125711299, 100154063565, -81834448272, -147586010830}

Mathematica

Clear[p, x, n];
<< DiscreteMath`Combinatorica`
p[x_, n_] = Sum[Eulerian[n+1, k]*(-x)^k*Sum[StirlingS2[n, m]*x^m, {m, 0, n - k}], {k, 0, n}];
Table[CoefficientList[p[x, n], x], {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A161129 A011074 A020816 * A157391 A099097 A152150

Adjacent sequences: A174857 A174858 A174859 * A174861 A174862 A174863

Keyword

sign,tabl,uned

Author

Roger L. Bagula, Mar 31 2010

Status

approved