cp's OEIS Frontend

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

%I A081108 #27 Mar 04 2023 05:56:13
%S A081108 1,9,80,704,6144,53248,458752,3932160,33554432,285212672,2415919104,
%T A081108 20401094656,171798691840,1443109011456,12094627905536,
%U A081108 101155069755392,844424930131968,7036874417766400,58546795155816448,486388759756013568
%N A081108 8th binomial transform of (1,1,0,0,0,0,...).
%C A081108 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
%H A081108 Vincenzo Librandi, <a href="/A081108/b081108.txt">Table of n, a(n) for n = 0..300</a>
%H A081108 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16,-64).
%F A081108 a(n) = 16*a(n-1) - 64*a(n-2), a(0) = 1, a(1) = 9.
%F A081108 a(n) = (n + 8)*8^(n-1).
%F A081108 G.f.: (1 - 7*x)/(1 - 8*x)^2.
%F A081108 E.g.f.: exp(8*x)*(1 + x). - _Stefano Spezia_, Mar 04 2023
%t A081108 LinearRecurrence[{16,-64},{1,9},30] (* _Harvey P. Dale_, Jun 11 2013 *)
%t A081108 CoefficientList[Series[(1 - 7 x) / (1 - 8 x)^2, {x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 06 2013 *)
%o A081108 (Magma) [(n+8)*8^(n-1): n in [0..25]]; // _Vincenzo Librandi_, Aug 06 2013
%o A081108 (PARI) a(n)=(n+8)*8^(n-1) \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A081108 Cf. A081107, A081109, A006234.
%K A081108 easy,nonn
%O A081108 0,2
%A A081108 _Paul Barry_, Mar 07 2003