A170749 Expansion of g.f.: (1+x)/(1-29*x).

1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379276070, 12621216999006030, 366015292971174870, 10614443496164071230, 307818861388758065670, 8926746980273983904430, 258875662427945533228470

Offset

0,2

Links

Kenny Lau, Table of n, a(n) for n = 0..683

Index entries for linear recurrences with constant coefficients, signature (29).

Formula

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*30^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n > 0, a(n) = 30*29^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f.: (30*exp(29*x) -1)/29. - G. C. Greubel, Sep 25 2019

Maple

k:=30; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 25 2019

Mathematica

With[{k=30}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Sep 25 2019 *)
Join[{1}, NestList[29#&, 30, 20]] (* Harvey P. Dale, Aug 27 2020 *)

Prog

(Python) for i in range(31):print(i, 30*29**(i-1) if i>0 else 1) # Kenny Lau, Aug 03 2017
(PARI) vector(26, n, k=30; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 25 2019
(Magma) k:=30; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 25 2019
(Sage) k=30; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 25 2019
(GAP) k:=30;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 25 2019

Crossrefs

Cf. A003945, A097805.

Sequence in context: A170615 A170663 A170711 * A218732 A158580 A171335

Adjacent sequences: A170746 A170747 A170748 * A170750 A170751 A170752

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 04 2009

Status

approved