A170759 Expansion of g.f.: (1+x)/(1-39*x).

1, 40, 1560, 60840, 2372760, 92537640, 3608967960, 140749750440, 5489240267160, 214080370419240, 8349134446350360, 325616243407664040, 12699033492898897560, 495262306223057004840, 19315229942699223188760, 753293967765269704361640

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..600

Index entries for linear recurrences with constant coefficients, signature (39).

Formula

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*40^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 40*39^(n-1). - Vincenzo Librandi, Dec 05 2009

a(0)=1, a(1)=40, a(n) = 39*a(n-1). - Vincenzo Librandi, Dec 10 2012

E.g.f.: (40*exp(39*x) - 1)/39. - G. C. Greubel, Oct 10 2019

Maple

k:=40; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 10 2019

Mathematica

CoefficientList[Series[(1+x)/(1-39*x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 10 2012 *)
With[{k = 40}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 10 2019 *)

Prog

(Magma) [1] cat [40*39^(n-1): n in [1..20]]; // Vincenzo Librandi, Dec 11 2012
(PARI) vector(26, n, k=40; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 10 2019
(Sage) k=40; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Oct 10 2019
(GAP) k:=40;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019

Crossrefs

Cf. A003945.

Sequence in context: A170673 A170721 A063820 * A218742 A158703 A209223

Adjacent sequences: A170756 A170757 A170758 * A170760 A170761 A170762

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 04 2009

Status

approved