A020976 Expansion of 1/((1-8*x)*(1-9*x)*(1-10*x)).

1, 27, 487, 7335, 99631, 1265607, 15341887, 179688375, 2050086511, 22913907687, 251930201887, 2733012078615, 29322230800591, 311701053949767, 3287717299503487, 34448718207176055, 358912563957741871

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (27, -242, 720).

Formula

If we define f(m,j,x)=sum(binomial(m,k)*stirling2(k,j)*x^(m-k),k=j..m) then a(n-2)=f(n,2,8), (n>=2). - Milan Janjic, Apr 26 2009

From Harvey P. Dale, Oct 25 2011: (Start)

a(0) = 1, a(1) = 27, a(2) = 487, a(n) = 27*a(n-1)-242*a(n-2)+720*a(n-3).

a(n) = 2^(2+3*(n+1))+2^(n+1)*5^(2+n)-9^(2+n). (End)

Maple

a:=seq(2^(2+3*(n+1))+2^(n+1)*5^(2+n)-9^(2+n), n=0..16); # Muniru A Asiru, Feb 10 2018

Mathematica

CoefficientList[Series[1/((1-8x)(1-9x)(1-10x)), {x, 0, 20}], x] (* or *)
LinearRecurrence[{27, -242, 720}, {1, 27, 487}, 20] (* or *)
Table[2^(3n+2)+ 2^n 5^(n+1)- 9^(n+1), {n, 20}] (* Harvey P. Dale, Oct 25 2011 *)

Prog

(Magma) [2^(2+3*(n+1))+2^(n+1)*5^(n+2)-9^(n+2): n in [0..30]]; // Vincenzo Librandi, Oct 26 2011
(PARI) x='x+O('x^30); Vec(1/((1-8*x)*(1-9*x)*(1-10*x))) \\ G. C. Greubel, Feb 09 2018
(GAP) a:=[1, 27, 487];; for n in [4..17] do a[n]:=27*a[n-1]-242*a[n-2]+720*a[n-3]; od; # Muniru A Asiru, Feb 10 2018

Crossrefs

Sequence in context: A024346 A025983 A081139 * A024114 A025982 A042408

Adjacent sequences: A020973 A020974 A020975 * A020977 A020978 A020979

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Typo in formula fixed by Vincenzo Librandi, Oct 26 2011

Status

approved