A021049 Expansion of 1/((1-x)*(1-2*x)*(1-3*x)*(1-10*x)).

1, 16, 185, 1940, 19701, 197976, 1982785, 19837180, 198400301, 1984089536, 19841156985, 198412358820, 1984125963301, 19841266774696, 198412689204785, 1984126956486860, 19841269758316701, 198412698163773456

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (16,-71,116,-60).

Formula

a(n) = -(1/18)+2^n-(27/14)*3^n+(125/63)*10^n. - Antonio Alberto Olivares, May 22 2012

a(0)=1, a(1)=16; for n>1, a(n) = 13*a(n-1) -30*a(n-2) +2^n - 1. - Vincenzo Librandi, Jul 05 2013

a(0)=1, a(1)=16, a(2)=185, a(3)=1940; for n>3, a(n) = 16*a(n-1) -71*a(n-2) +116*a(n-3) -60*a(n-4). - Vincenzo Librandi, Jul 05 2013

E.g.f.: exp(x)*(250*exp(9*x) - 243*exp(2*x) + 126*exp(x) - 7)/126. - Stefano Spezia, Apr 30 2025

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 3 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 05 2013 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-3*x)*(1-10*x)))); // Vincenzo Librandi, Jul 05 2013
(Magma) I:=[1, 16, 185, 1940]; [n le 4 select I[n] else 16*Self(n-1)-71*Self(n-2)+116*Self(n-3)-60*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 05 2013

Crossrefs

Sequence in context: A125428 A203391 A016249 * A067308 A387234 A016244

Adjacent sequences: A021046 A021047 A021048 * A021050 A021051 A021052

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved