A081043 8th binomial transform of (1,7,0,0,0,0,0,...).
1, 15, 176, 1856, 18432, 176128, 1638400, 14942208, 134217728, 1191182336, 10468982784, 91268055040, 790273982464, 6803228196864, 58274116272128, 496979255754752, 4222124650659840, 35747322042253312, 301741175033823232
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (16,-64).
Programs
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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
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Mathematica
LinearRecurrence[{16,-64},{1,15},20] (* or *) Table[(7n+8)8^(n-1),{n,0,20}] (* Harvey P. Dale, Feb 22 2012 *)
Formula
a(n) = 16*a(n-1) - 64*a(n-2), a(0)=1, a(1)=15.
a(n) = (7n+8)*8^(n-1).
a(n) = Sum_{k=0..n} (k+1)*7^k*binomial(n, k).
G.f.: (1-x)/(1-8*x)^2.
E.g.f.: exp(8*x)*(1 + 7*x). - Stefano Spezia, Jan 31 2025