A129008 a(n) = (n^3 + n^2)*8^n.
16, 768, 18432, 327680, 4915200, 66060288, 822083584, 9663676416, 108716359680, 1181116006400, 12472585027584, 128642860449792, 1300722255659008, 12930256742645760, 126663739519795200, 1224979098644774912
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (32,-384,2048,-4096).
Programs
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Magma
[(n^3+n^2)*8^n: n in [1..25]]; // Vincenzo Librandi, Feb 12 2013
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Magma
I:=[16, 768, 18432, 327680]; [n le 4 select I[n] else 32*Self(n-1)-384*Self(n-2)+2048*Self(n-3)-4096*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Feb 12 2013
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Mathematica
CoefficientList[Series[16 (1 + 16 x)/(1 - 8 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 12 2013 *) LinearRecurrence[{32,-384,2048,-4096},{16,768,18432,327680},20] (* Harvey P. Dale, Jun 24 2025 *)
Formula
G.f.: 16*x*(1 + 16*x)/(1 - 8*x)^4. - Vincenzo Librandi, Feb 12 2013
a(n) = 32*a(n-1)-384*a(n-2)+2048*a(n-3)-4096*a(n-4). - Vincenzo Librandi, Feb 12 2013