A020570 Expansion of 1/((1-6*x)*(1-7*x)*(1-8*x)).

1, 21, 295, 3465, 36751, 365001, 3463615, 31794105, 284628751, 2499039081, 21606842335, 184519243545, 1559982264751, 13079717026761, 108915112739455, 901732722577785, 7429565635164751, 60963378722560041, 498496565225842975, 4064108629664292825, 33049477950757248751

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (21,-146,336).

Formula

If we define f(m,j,x) = Sum_{k=j..m} (binomial(m,k)*stirling2(k,j)*x^(m-k)) then a(n-2)=f(n,2,6), (n>=2). - Milan Janjic, Apr 26 2009

a(n) = 18*6^n -49*7^n +32*8^n. - R. J. Mathar, Jun 30 2013

a(0)=1, a(1)=21, a(2)=295; for n>2, a(n) = 21*a(n-1) -146*a(n-2) +336*a(n-3). - Vincenzo Librandi, Jul 04 2013

a(n) = 15*a(n-1) -56*a(n-2) +6^n. - Vincenzo Librandi, Jul 04 2013

Mathematica

CoefficientList[Series[1/((1-6*x)*(1-7*x)*(1-8*x)), {x, 0, 20}], x]  (* Harvey P. Dale, Feb 24 2011 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-6*x)*(1-7*x)*(1-8*x)))); /* or */ I:=[1, 21, 295]; [n le 3 select I[n] else 21*Self(n-1)-146*Self(n-2)+336*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 04 2013
(PARI) x='x+O('x^30); Vec(1/((1-6*x)*(1-7*x)*(1-8*x))) \\ G. C. Greubel, Feb 07 2018

Crossrefs

Sequence in context: A081137 A027474 A021864 * A025940 A041844 A295779

Adjacent sequences: A020567 A020568 A020569 * A020571 A020572 A020573

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved