A081108 8th binomial transform of (1,1,0,0,0,0,...).

1, 9, 80, 704, 6144, 53248, 458752, 3932160, 33554432, 285212672, 2415919104, 20401094656, 171798691840, 1443109011456, 12094627905536, 101155069755392, 844424930131968, 7036874417766400, 58546795155816448, 486388759756013568

Offset

0,2

Comments

Main diagonal of array defined by m(0,j) = j; m(i,0) = i and m(i,j) = m(i-1,j) + 7*m(i-1,j-1). - Benoit Cloitre, Jun 13 2003

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (16,-64).

Formula

a(n) = 16*a(n-1) - 64*a(n-2), a(0) = 1, a(1) = 9.

a(n) = (n + 8)*8^(n-1).

G.f.: (1 - 7*x)/(1 - 8*x)^2.

E.g.f.: exp(8*x)*(1 + x). - Stefano Spezia, Mar 04 2023

Mathematica

LinearRecurrence[{16, -64}, {1, 9}, 30] (* Harvey P. Dale, Jun 11 2013 *)
CoefficientList[Series[(1 - 7 x) / (1 - 8 x)^2, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)

Prog

(Magma) [(n+8)*8^(n-1): n in [0..25]]; // Vincenzo Librandi, Aug 06 2013
(PARI) a(n)=(n+8)*8^(n-1) \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A081107, A081109, A006234.

Sequence in context: A275497 A171314 A370039 * A176174 A242632 A018913

Adjacent sequences: A081105 A081106 A081107 * A081109 A081110 A081111

Keyword

easy,nonn

Author

Paul Barry, Mar 07 2003

Status

approved