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

Author

N. J. A. Sloane, Dec 04 2009

Keywords

• nonn
• easy

Links

• Kenny Lau, Table of n, a(n) for n = 0..683
• Index entries for linear recurrences with constant coefficients, signature (29).

Crossrefs

Cf. A003945, A097805.

Programs

GAP

k:=30;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # 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

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 *)

PARI

vector(26, n, k=30; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 25 2019

Python

for i in range(31):print(i,30*29**(i-1) if i>0 else 1) # Kenny Lau, Aug 03 2017

Sage

k=30; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 25 2019

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