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A136160 Triangle T(n,k) = k*A053120(n,k). 0
1, 0, 4, -3, 0, 12, 0, -16, 0, 32, 5, 0, -60, 0, 80, 0, 36, 0, -192, 0, 192, -7, 0, 168, 0, -560, 0, 448, 0, -64, 0, 640, 0, -1536, 0, 1024, 9, 0, -360, 0, 2160, 0, -4032, 0, 2304, 0, 100, 0, -1600, 0, 6720, 0, -10240, 0, 5120, -11, 0, 660, 0, -6160, 0, 19712, 0, -25344, 0, 11264 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The definition is equivalent to building the derivatives of the Chebyshev polynomials T(n,x) and listing the coefficients [x^k] dT/dx in row n.

Row sums are the squares A000079(n-1).

Obtained from A136265 by sign flips and nulling each second diagonal. - R. J. Mathar, Sep 04 2011

REFERENCES

Harry Hochstadt, The Functions of Mathematical Physics, Dover, New York, 1986, page 8 and pages 42 - 43

LINKS

Table of n, a(n) for n=1..66.

Peter Steinbach, Golden fields: a case for the heptagon, Math. Mag. Vol. 70, No. 1, Feb. 1997, 22-31.

EXAMPLE

1;

0, 4;

-3, 0, 12;

0, -16, 0, 32;

5, 0, -60, 0, 80;

0, 36, 0, -192, 0, 192;

-7, 0, 168, 0, -560, 0, 448;

0, -64, 0, 640, 0, -1536,0, 1024;

9, 0, -360, 0, 2160,0, -4032, 0, 2304;

0, 100, 0, -1600, 0, 6720, 0, -10240, 0, 5120;

-11, 0, 660, 0, -6160, 0, 19712, 0, -25344, 0, 11264;

MATHEMATICA

P[x, 0] = 1; P[x, 1] = x; P[x_, n_] := P[x, n] = 2*x*P[x, n - 1] - P[x, n - 2]; Q[x_, n_] := D[P[x, n + 1], x]; a = Table[CoefficientList[Q[x, n], x], {n, 0, 10}]; Flatten[a]

CROSSREFS

Cf. A053120, A135929.

Sequence in context: A176214 A011091 A335821 * A268439 A120362 A201636

Adjacent sequences:  A136157 A136158 A136159 * A136161 A136162 A136163

KEYWORD

uned,tabl,sign

AUTHOR

Roger L. Bagula, Mar 16 2008

STATUS

approved

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Last modified August 5 07:54 EDT 2021. Contains 346464 sequences. (Running on oeis4.)