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A209404 Negated coefficients of Chebyshev T polynomials: a(n) = -A053120(n+14, n), n >= 0. 3
1, 15, 128, 816, 4320, 20064, 84480, 329472, 1208064, 4209920, 14057472, 45260800, 141213696, 428654592, 1270087680, 3683254272, 10478223360, 29297934336, 80648077312, 218864025600, 586290298880, 1551944908800, 4063273943040 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The MAGMA program provided calculates the coefficients of order one Chebyshev polynomials, for any arbitrary level. For example, setting Rn to 0 produces A001792, 1 produces A001793, 2 produces A001794, 3 produces A006974, 4 produces A006975, and 5 produces A006976. This sequence is produced with an Rn of 6.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (16,-112,448,-1120,1792,-1792,1024,-256).

FORMULA

a(n) = 2^(n-1)*binomial(n+6, 6)*(n+14)/7 = -A053120(n+14, n), n >= 0. [See a comment in A053120 on subdiagonal sequences. - Wolfdieter Lang, Jan 03 2020]

G.f.: (1-x)/(1-2*x)^8. - Colin Barker, May 31 2013

E.g.f.: (1/315)*exp(2*x)*(315 + 4095*x + 11340*x^2 + 11550*x^3 + 5250*x^4 + 1134*x^5 + 112*x^6 + 4*x^7). - Stefano Spezia, Oct 17 2019

MAPLE

seq(2^(n-1)*(n+14)*binomial(n+6, 6)/7, n=0..30); # G. C. Greubel, Oct 18 2019

MATHEMATICA

CoefficientList[Series[(1-x)/(1-2*x)^8, {x, 0, 30}], x] (* or *) Table[2^(n-1)*Binomial[n+6, 6]*(n+14)/7, {n, 0, 30}] (* G. C. Greubel, Jan 03 2018 *)

PROG

(MAGMA) Rn:=6; [2^(n-1)/(Rn+1)*Binomial(n+Rn, Rn)*(n+(Rn+1)*2) : n in [0..22]];

(PARI) for(n=0, 30, print1(2^(n-1)*binomial(n+6, 6)*(n+14)/7, ", ")) \\ G. C. Greubel, Jan 03 2018

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 23); Coefficients(R!( (1-x)/(1-2*x)^8 )); // Marius A. Burtea, Oct 17 2019

(GAP) List([0..30], n-> 2^(n-1)*(n+14)*Binomial(n+6, 6)/7); # G. C. Greubel, Oct 18 2019

CROSSREFS

Cf. A001792, A001793, A001794, A006974, A006975, A006976, A053120.

Sequence in context: A073509 A198850 A283120 * A127595 A056579 A294054

Adjacent sequences:  A209401 A209402 A209403 * A209405 A209406 A209407

KEYWORD

nonn,easy

AUTHOR

Brad Clardy, Mar 08 2012

EXTENSIONS

Name made more specific by Wolfdieter Lang, Nov 25 2019

STATUS

approved

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Last modified February 27 10:31 EST 2020. Contains 332304 sequences. (Running on oeis4.)