

A072335


Expansion of 1/((1x^2)*(14*x+x^2)).


5



1, 4, 16, 60, 225, 840, 3136, 11704, 43681, 163020, 608400, 2270580, 8473921, 31625104, 118026496, 440480880, 1643897025, 6135107220, 22896531856, 85451020204, 318907548961, 1190179175640, 4441809153600, 16577057438760, 61866420601441, 230888624967004
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OFFSET

0,2


LINKS

Table of n, a(n) for n=0..25.
M. R. Bremner, Free associative algebras, noncommutative Grobner bases, and universal associative envelopes for nonassociative structures, arXiv preprint arXiv:1303.0920, 2013
N. J. A. Sloane, Transforms
Index entries for sequences related to Chebyshev polynomials.
Index entries for linear recurrences with constant coefficients, signature (4,0,4,1).


FORMULA

a(n) = (1/12)*((74*sqrt(3))*(2sqrt(3))^n+(7+4*sqrt(3))*(2+sqrt(3))^n3+(1)^n). Recurrence: a(n) = 4*a(n1)4*a(n3)+a(n4).
a(n)=sum{k=0..floor(n/2), U(n2k, 2)}  Paul Barry, Nov 15 2003
The g.f. can also be written as 1/(14*x+4*x^3x^4), which relates this sequence to the family of sequences described in A225682.


MATHEMATICA

CoefficientList[Series[1/((1x^2)*(14x+x^2)), {x, 0, 30}], x] (* or *) LinearRecurrence[{4, 0, 4, 1}, {1, 4, 16, 60}, 30] (* Harvey P. Dale, Aug 22 2015 *)


PROG

(PARI) Vec(1/((1x^2)*(14*x+x^2))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012


CROSSREFS

EULER transform of A072279 (with its initial 1 omitted).
A001353(n)^2 is a bisection of a(n).
Cf. A225682.
Sequence in context: A269673 A231896 A128650 * A081161 A032106 A269462
Adjacent sequences: A072332 A072333 A072334 * A072336 A072337 A072338


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Jul 15 2002


STATUS

approved



