A028574 Expansion of 1/((1-16*x)^2*(1 - 14*x + 56*x^2 - 64*x^3)).

1, 46, 1356, 32856, 714672, 14543712, 283133632, 5342645632, 98527058688, 1785505986048, 31916125744128, 564249389488128, 9885635491508224, 171893957900591104, 2969895694579974144, 51031902826852614144, 872728343238158254080

Offset

0,2

Comments

The original o.g.f. was transferred to sequence A308436.

Links

G. C. Greubel, Table of n, a(n) for n = 0..820

Index entries for linear recurrences with constant coefficients, signature (46,-760,5440,-16384,16384).

Formula

From G. C. Greubel, May 28 2019: (Start)

a(n) = 2^n*(3 - 49*2^(n+1) + 147*2^(2*n+3) + (21*n -10)*2^(3*n+6))/441.

E.g.f.: (3 - 98*exp(2*x) + 1176*exp(6*x) + 128*(-5 + 168*x)*exp(14*x) )*exp(2*x)/441. (End)

Mathematica

CoefficientList[Series[1/((1-16*x)^2*(1-14*x+56*x^2-64*x^3)), {x, 0, 20}], x] (* G. C. Greubel, May 28 2019 *)

Prog

(PARI) my(x='x+O('x^20)); Vec(1/((1-16*x)^2*(1-14*x+56*x^2-64*x^3))) \\ G. C. Greubel, May 28 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( 1/((1-16*x)^2*(1-14*x+56*x^2-64*x^3)) )); // G. C. Greubel, May 28 2019
(Sage) (1/((1-16*x)^2*(1-14*x+56*x^2-64*x^3))).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 28 2019

Crossrefs

Cf. A308436.

Sequence in context: A188412 A066403 A286788 * A302767 A078195 A103725

Adjacent sequences: A028571 A028572 A028573 * A028575 A028576 A028577

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Original name and explicit formula of Yahia Kahloune moved to A308436.

G.f. corrected by Georg Fischer, May 27 2019

Status

approved