%I #18 Sep 08 2022 08:44:50

%S 1,46,1356,32856,714672,14543712,283133632,5342645632,98527058688,

%T 1785505986048,31916125744128,564249389488128,9885635491508224,

%U 171893957900591104,2969895694579974144,51031902826852614144,872728343238158254080

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

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

%H G. C. Greubel, <a href="/A028574/b028574.txt">Table of n, a(n) for n = 0..820</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (46,-760,5440,-16384,16384).

%F From _G. C. Greubel_, May 28 2019: (Start)

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

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

%t 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 *)

%o (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

%o (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

%o (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

%Y Cf. A308436.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

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

%E G.f. corrected by _Georg Fischer_, May 27 2019