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A099599 Triangle T read by rows: coefficients of polynomials generating array A099597. 3
1, 1, 1, 1, 0, 2, 1, 9, -12, 6, 1, -104, 204, -120, 24, 1, 2265, -4840, 3540, -1080, 120, 1, -71064, 164910, -138840, 54360, -10080, 720, 1, 3079825, -7626948, 7134330, -3300360, 808920, -100800, 5040, 1, -176449776, 460982648, -468313104 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Row sums are k (A000027), left edge columns are factorials (A000142). [Peter Bala, Aug 19 2013]

LINKS

Table of n, a(n) for n=0..39.

FORMULA

The row polynomials satisfy the second order recurrence equation R(n,x) = (n*x+1)*R(n-1,x-1) - (n-1)*(x-1)*R(n-2,x-2), with the initial conditions R(0,x) = 1 and R(1,x) = 1+x. - Peter Bala, Aug 19 2013

EXAMPLE

1

x + 1

2*x^2 + 1

6*x^3 - 12*x^2 + 9*x + 1

24*x^4 - 120*x^3 + 204*x^2 - 104*x + 1

120*x^5 - 1080*x^4 + 3540*x^3 - 4840*x^2 + 2265*x + 1

MAPLE

#A099599 Define row polynomials R(n, x) recursively

R := proc(n, x) option remember;

if n = 0 then 1 elif n = 1 then 1+x

else (nx+1)thisproc(n-1, x-1) - (n-1)(x-1)thisproc(n-2, x-2);

fi

end:

with(PolynomialTools):

seq(CoefficientList(R(n, x), x), n = 0..10);

# Peter Bala, Aug 19 2013

CROSSREFS

Sequence in context: A240085 A078623 A198204 * A085488 A072265 A192352

Adjacent sequences:  A099596 A099597 A099598 * A099600 A099601 A099602

KEYWORD

sign,tabl

AUTHOR

Ralf Stephan, Oct 28 2004

STATUS

approved

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Last modified October 16 08:50 EDT 2019. Contains 328056 sequences. (Running on oeis4.)