A170754 Expansion of g.f.: (1+x)/(1-34*x).

1, 35, 1190, 40460, 1375640, 46771760, 1590239840, 54068154560, 1838317255040, 62502786671360, 2125094746826240, 72253221392092160, 2456609527331133440, 83524723929258536960, 2839840613594790256640, 96554580862222868725760, 3282855749315577536675840

Offset: 0

Author

N. J. A. Sloane, Dec 04 2009

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..649
• Index entries for linear recurrences with constant coefficients, signature (34).

Crossrefs

Cf. A003945.

Programs

GAP

k:=35;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 09 2019

Magma

k:=35; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 09 2019

Maple

k:=35; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 09 2019

Mathematica

CoefficientList[Series[(1+x)/(1-34x),{x,0,30}],x] (* Harvey P. Dale, Aug 23 2016 *)
With[{k = 35}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 09 2019 *)

PARI

vector(26, n, k=35; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 09 2019

Sage

k=35; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Oct 09 2019

Formula

a(n)= Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*35^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 35*34^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f.: (1/34)*(35*exp(34*x) - 1). - Stefano Spezia, Oct 09 2019