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A181472 Riordan array ((1+x)/(1+2x+2x^2),x(1+x)/(1+2x+2x^2)). 2
1, -1, 1, 0, -2, 1, 2, 1, -3, 1, -4, 4, 3, -4, 1, 4, -12, 5, 6, -5, 1, 0, 16, -24, 4, 10, -6, 1, -8, -4, 42, -39, 0, 15, -7, 1, 16, -32, -24, 88, -55, -8, 21, -8, 1, -16, 80, -72, -80, 159, -69, -21, 28, -9, 1, 0, -96, 240, -112, -200, 258, -77, -40, 36, -10, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Inverse is A054336. Coefficient array for Faber polynomials (of second kind) defined by f(x)=x+1-sum{(-1)^k/x^k,k>=1}.

Subtriangle of the triangle given by (0, -1, 1, -2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. -Philippe Deléham, Feb 20 2013

LINKS

Table of n, a(n) for n=0..65.

FORMULA

T(n,m)=sum(k=m..m,(-2)^(k-m)*binomial(k,n-k)*binomial(k-1,m-1)), n,m>0, [From Vladimir Kruchinin, Mar 09 2011]

T(n,k) = T(n-1,k-1) + T(n-2,k-1) -2*T(n-1,k) - 2*T(n-2,k), T(0,0) = T(1,1) = 1, T(1,0) = -1, T(n,k) = 0 if k<0 or if k>n. -Philippe Deléham, Feb 20 2013

G.f.: (-1-x)/(-1-2*x-2*x^2+x*y+x^2*y). - R. J. Mathar, Aug 12 2015

EXAMPLE

Triangle begins

1,

-1, 1,

0, -2, 1,

2, 1, -3, 1,

-4, 4, 3, -4, 1,

4, -12, 5, 6, -5, 1,

0, 16, -24, 4, 10, -6, 1,

-8, -4, 42, -39, 0, 15, -7, 1,

16, -32, -24, 88, -55, -8, 21, -8, 1

Production matrix is

-1, 1,

-1, -1, 1,

0, -1, -1, 1,

-1, 0, -1, -1, 1,

0, -1, 0, -1, -1, 1,

-2, 0, -1, 0, -1, -1, 1,

0, -2, 0, -1, 0, -1, -1, 1,

-5, 0, -2, 0, -1, 0, -1, -1, 1,

0, -5, 0, -2, 0, -1, 0, -1, -1, 1

-14, 0, -5, 0, -2, 0, -1, 0, -1, -1, 1

based on the aerated Catalan numbers.

Triangle (0, -1, 1, -2, 0, 0, 0, ...) DELTA (1, 0, 0, 0, ...) begins:

1

0, 1

0, -1, 1

0, 0, -2, 1

0, 2, 1, -3, 1

0, -4, 4, 3, -4, 1

0, 4, -12, 5, 6, -5, 1. -Philippe Deléham, Feb 20 2013

CROSSREFS

Sequence in context: A153174 A138222 A138224 * A271825 A271875 A324194

Adjacent sequences:  A181469 A181470 A181471 * A181473 A181474 A181475

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Oct 21 2010

STATUS

approved

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Last modified November 17 13:33 EST 2019. Contains 329230 sequences. (Running on oeis4.)