A167602 - OEIS

%I #14 Jun 18 2016 00:43:44

%S 1,-14,124,-1112,11504,-121440,1235392,-12400000,125394688,

%T -1274938880,12949806080,-131304445952,1331250655232,-13503545892864,

%U 136990201856000,-1389579896979456,14094585311461376

%N Expansion of 1/(1+14*x+72*x^2+384*x^3+512*x^4).

%C The limit of a(n+1)/a(n) tends to 8*(-1.2679237217317025...).

%H G. C. Greubel, <a href="/A167602/b167602.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (-14,-72,-384,-512).

%F a(n+4) + 14*a(n+3) + 72*a(n+2) + 384*a(n+1) + 512*a(n) = 0. - _G. C. Greubel_, Jun 17 2016

%t Clear[p, q, x, t, n];

%t p[z_]:= 1 + 6 *z + 9 *z^2 + 14* z^3 + 8 *z^4;

%t q[x_]:= 1/Expand[x^4*p[1/x]];

%t a = Table[8^(n + 1)*SeriesCoefficient[ Series[q[t], {t, 0, 60}], n], {n, 0, 60}]

%t LinearRecurrence[{-14, -72, -384, -512}, {1, -14, 124, -1112}, 100] (* _G. C. Greubel_, Jun 17 2016 *)

%o (PARI) Vec(1/(1+14*x+72*x^2+384*x^3+512*x^4)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012

%K sign,easy

%O 0,2

%A _Roger L. Bagula_, Nov 06 2009

%E Definition rephrased. - _R. J. Mathar_, Jul 02 2012