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A112552 A modified Chebyshev transform of the second kind. 6
1, 0, 1, -2, 0, 1, 0, -3, 0, 1, 3, 0, -4, 0, 1, 0, 6, 0, -5, 0, 1, -4, 0, 10, 0, -6, 0, 1, 0, -10, 0, 15, 0, -7, 0, 1, 5, 0, -20, 0, 21, 0, -8, 0, 1, 0, 15, 0, -35, 0, 28, 0, -9, 0, 1, -6, 0, 35, 0, -56, 0, 36, 0, -10, 0, 1, 0, -21, 0, 70, 0, -84, 0, 45, 0, -11, 0, 1, 7, 0, -56, 0, 126, 0, -120, 0, 55, 0, -12, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Row sums are A112553. Inverse is A112554. Riordan array product (1/(1+x^2),x)(1/(1+x^2),x/(1+x^2)).

LINKS

Table of n, a(n) for n=0..90.

FORMULA

Riordan array (1/(1+x^2)^2, x/(1+x^2)); Number triangle T(n, k)=(-1)^(n-k)*sum{j=0..n, (1+(-1)^(n-j))(1+(-1)^(j-k))C((j+k)/2, k)/4}.

Unsigned triangle = A128174 * A149310, as infinite lower triangular matrices, with row sums A052952: (1, 1, 3, 4, 8, 12, 21, 33,...). - Gary W. Adamson, Oct 28 2007

EXAMPLE

Triangle begins

.1;

.0,1;

.-2,0,1;

.0,-3,0,1;

.3,0,-4,0,1;

.0,6,0,-5,0,1;

.-4,0,10,0,-6,0,1;

CROSSREFS

Cf. A128174, A049310, A052952.

Sequence in context: A298972 A143728 A127368 * A048154 A320602 A134511

Adjacent sequences:  A112549 A112550 A112551 * A112553 A112554 A112555

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Sep 13 2005

STATUS

approved

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Last modified November 13 00:25 EST 2019. Contains 329083 sequences. (Running on oeis4.)