login
A081108
8th binomial transform of (1,1,0,0,0,0,...).
5
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
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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 07 2003
STATUS
approved