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A081043 8th binomial transform of (1,7,0,0,0,0,0,...).

%I A081043 #26 Jan 31 2025 15:06:29
%S A081043 1,15,176,1856,18432,176128,1638400,14942208,134217728,1191182336,
%T A081043 10468982784,91268055040,790273982464,6803228196864,58274116272128,
%U A081043 496979255754752,4222124650659840,35747322042253312,301741175033823232
%N A081043 8th binomial transform of (1,7,0,0,0,0,0,...).
%H A081043 Vincenzo Librandi, <a href="/A081043/b081043.txt">Table of n, a(n) for n = 0..200</a>
%H A081043 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16,-64).
%F A081043 a(n) = 16*a(n-1) - 64*a(n-2), a(0)=1, a(1)=15.
%F A081043 a(n) = (7n+8)*8^(n-1).
%F A081043 a(n) = Sum_{k=0..n} (k+1)*7^k*binomial(n, k).
%F A081043 G.f.: (1-x)/(1-8*x)^2.
%F A081043 E.g.f.: exp(8*x)*(1 + 7*x). - _Stefano Spezia_, Jan 31 2025
%t A081043 LinearRecurrence[{16,-64},{1,15},20] (* or *) Table[(7n+8)8^(n-1),{n,0,20}] (* _Harvey P. Dale_, Feb 22 2012 *)
%o A081043 (Magma) I:=[1, 15]; [n le 2 select I[n] else 16*Self(n-1)-64*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Feb 23 2012
%Y A081043 Cf. A081042, A081044.
%K A081043 easy,nonn
%O A081043 0,2
%A A081043 _Paul Barry_, Mar 04 2003