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A002700 Coefficients of Chebyshev polynomials: n*(2*n+1) * 4^(n-1).
(Formerly M3147 N1275)
6
3, 40, 336, 2304, 14080, 79872, 430080, 2228224, 11206656, 55050240, 265289728, 1258291200, 5888802816, 27246198784, 124822487040, 566935683072, 2555505541120, 11441792876544, 50921132261376, 225399883694080, 992858999881728, 4354066045992960 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

C. Lanczos, Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 518.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

C. Lanczos, Applied Analysis (Annotated scans of selected pages)

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (12,-48,64).

FORMULA

a(n) = 12*a(n-1) - 48*a(n-2) + 64*a(n-3). - Colin Barker, Jun 15 2015

a(n) = 1/2*Sum_{k = 0..2*n} k^2*binomial(2*n,k). Cf. A002699. - Peter Bala, Apr 09 2017

MAPLE

A002700:=-(3+4*z)/(4*z-1)**3; # Simon Plouffe in his 1992 dissertation.

MATHEMATICA

Table[n*(2*n+1)*2^(2*n-2), {n, 1, 30}] (* Vaclav Kotesovec, Jun 03 2014 *)

LinearRecurrence[{12, -48, 64}, {3, 40, 336}, 30] (* Harvey P. Dale, May 17 2018 *)

PROG

(PARI) Vec(-x*(4*x+3)/(4*x-1)^3 + O(x^30)) \\ Colin Barker, Jun 15 2015

(MAGMA) [4^(n-1)*n*(2*n+1): n in [1..30]]; // G. C. Greubel, Jul 23 2019

(Sage) [4^(n-1)*n*(2*n+1) for n in (1..30)] # G. C. Greubel, Jul 23 2019

(GAP) List([1..30], n-> 4^(n-1)*n*(2*n+1)); # G. C. Greubel, Jul 23 2019

CROSSREFS

Cf. A002699.

Sequence in context: A165395 A165386 A293501 * A220639 A005724 A215196

Adjacent sequences:  A002697 A002698 A002699 * A002701 A002702 A002703

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 21 06:00 EST 2019. Contains 329350 sequences. (Running on oeis4.)