A176664 A leading coefficient adjusted symmetrical triangle of polynomial coefficients based on:p(x,n)=Sum[k!*Binomial[x, k], {k, 0, n}]

1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -10, 17, -10, 1, 1, 10, -12, -12, 10, 1, 1, -115, 308, -391, 308, -115, 1, 1, 599, -1371, 769, 769, -1371, 599, 1, 1, -4448, 11838, -13503, 12219, -13503, 11838, -4448, 1, 1, 35864, -97529, 102186, -40525, -40525, 102186

Offset

0,12

Comments

Row sums are:

{1, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7,...}.

Links

Table of n, a(n) for n=0..51.

Formula

p(x,n)=Sum[k!*Binomial[x, k], {k, 0, n}];

t(n,m)=coefficients(p(x,n))+reverse(coefficients(p(x,n)))-1

Example

{1},
{1, 1},
{1, -1, 1},
{1, -1, -1, 1},
{1, -10, 17, -10, 1},
{1, 10, -12, -12, 10, 1},
{1, -115, 308, -391, 308, -115, 1},
{1, 599, -1371, 769, 769, -1371, 599, 1},
{1, -4448, 11838, -13503, 12219, -13503, 11838, -4448, 1},
{1, 35864, -97529, 102186, -40525, -40525, 102186, -97529, 35864, 1},
{1, -327025, 929363, -1075211, 721544, -497351, 721544, -1075211, 929363, -327025, 1}

Mathematica

Clear[p, x, n]
p[x_, n_] := Sum[k!*Binomial[x, k], {k, 0, n}];
Table[CoefficientList[ExpandAll[p[x, n]], x] + Reverse[CoefficientList[ ExpandAll[p[x, n]], x]] - 1, {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A167331 A255531 A157159 * A256346 A079630 A175389

Adjacent sequences: A176661 A176662 A176663 * A176665 A176666 A176667

Keyword

sign,tabl,uned

Author

Roger L. Bagula, Apr 23 2010

Status

approved