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

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (40).

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

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 *)

Prog

(PARI) vector(26, n, k=41; if(n==1, 1, k*(k-1)^(n-2))) \\ 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
(Sage) k=41; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Oct 10 2019
(GAP) k:=41;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019

Crossrefs

Cf. A003945.

Sequence in context: A170626 A170674 A170722 * A167957 A218743 A009985

Adjacent sequences: A170757 A170758 A170759 * A170761 A170762 A170763

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 04 2009

Status

approved