A170736 Expansion of g.f.: (1+x)/(1-16*x).

1, 17, 272, 4352, 69632, 1114112, 17825792, 285212672, 4563402752, 73014444032, 1168231104512, 18691697672192, 299067162755072, 4785074604081152, 76561193665298432, 1224979098644774912, 19599665578316398592, 313594649253062377472, 5017514388048998039552

Offset: 0

Author

N. J. A. Sloane, Dec 04 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..800
• Index entries for linear recurrences with constant coefficients, signature (16).

Crossrefs

Cf. A003945, A097805.

Programs

GAP

k:=17;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 24 2019

Magma

[1] cat [17*16^(n-1): n in [1..25]]; // Vincenzo Librandi, Dec 11 2012

Maple

k:=17; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 24 2019

Mathematica

Join[{1},17*16^Range[0,25]] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)
CoefficientList[Series[(1+x)/(1-16*x), {x, 0, 25}], x] (* Vincenzo Librandi, Dec 11 2012 *)

PARI

vector(26, n, k=17; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 24 2019

Sage

k=17; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 24 2019

Formula

a(n)= Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*17^k. - Philippe Deléham, Dec 04 2009

a(n) = 17*16^(n-1). - Vincenzo Librandi, Dec 11 2012

a(0)=1, a(1)=17, a(n) = 16*a(n-1). - Vincenzo Librandi, Dec 11 2012

E.g.f.: (17*exp(16*x) - 1)/16. - G. C. Greubel, Sep 24 2019