A170760 Expansion of g.f.: (1+x)/(1-40*x).

1, 41, 1640, 65600, 2624000, 104960000, 4198400000, 167936000000, 6717440000000, 268697600000000, 10747904000000000, 429916160000000000, 17196646400000000000, 687865856000000000000, 27514634240000000000000, 1100585369600000000000000

Offset: 0

Author

N. J. A. Sloane, Dec 04 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..600
• Index entries for linear recurrences with constant coefficients, signature (40).

Crossrefs

Cf. A003945.

Programs

GAP

k:=41;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019

Magma

k:=41; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 10 2019

Maple

k:=41; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 10 2019

Mathematica

CoefficientList[Series[(1+x)/(1-40*x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 10 2012 *)
With[{k = 41}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 10 2019 *)
Join[{1},NestList[40#&,41,20]] (* Harvey P. Dale, Jun 19 2023 *)

PARI

vector(26, n, k=41; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 10 2019

Sage

k=41; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Oct 10 2019

Formula

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*41^k. - Philippe Deléham, Dec 04 2009

a(0)=1; for n>0, a(n) = 41*40^(n-1). - Vincenzo Librandi, Dec 05 2009

a(0)=1, a(1)=41, a(n) = 40*a(n-1). - Vincenzo Librandi, Dec 10 2012

E.g.f.: (41*exp(40*x) - 1)/40. - G. C. Greubel, Oct 10 2019