A020782 Expansion of g.f. 1/((1-7*x)*(1-8*x)*(1-9*x)).

1, 24, 385, 5160, 62401, 706104, 7628545, 79669320, 810888001, 8089258584, 79415935105, 769621605480, 7379461252801, 70134974713464, 661651583000065, 6203106293141640, 57847125937972801, 537010118353326744, 4965807358070423425, 45765395460943045800, 420553385321258904001

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (24,-191,504).

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,2,7), (n>=2). - Milan Janjic, Apr 26 2009

From Vincenzo Librandi, Mar 15 2011: (Start)

a(n) = 24*a(n-1) - 191*a(n-2) + 504*a(n-3), n>=3.

a(n) = 17*a(n-1) - 72*a(n-2) + 7^n, n>=2. (End)

a(n) = 7^(n+2)/2 - 8^(n+2) + 9^(n+2)/2. - R. J. Mathar, Mar 15 2011

From Elmo R. Oliveira, Mar 26 2025: (Start)

E.g.f.: exp(7*x)*(49 - 128*exp(x) + 81*exp(2*x))/2.

a(n) = A005062(n+2) - A016149(n+1). (End)

Mathematica

CoefficientList[Series[1/((1-7x)(1-8x)(1-9x)), {x, 0, 20}], x] (* Harvey P. Dale, Aug 20 2013 *)
(* Alternative: *)
LinearRecurrence[{24, -191, 504}, {1, 24, 385}, 20] (* Harvey P. Dale, Aug 20 2013 *)

Crossrefs

Cf. A005062, A016149.

Sequence in context: A269181 A266185 A114631 * A025952 A028031 A042108

Adjacent sequences: A020779 A020780 A020781 * A020783 A020784 A020785

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Elmo R. Oliveira, Mar 26 2025

Status

approved