A170758 Expansion of g.f.: (1+x)/(1-38*x).

1, 39, 1482, 56316, 2140008, 81320304, 3090171552, 117426518976, 4462207721088, 169563893401344, 6443427949251072, 244850262071540736, 9304309958718547968, 353563778431304822784, 13435423580389583265792, 510546096054804164100096

Offset: 0

Author

N. J. A. Sloane, Dec 04 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (38).

Crossrefs

Cf. A003945.

Programs

GAP

k:=39;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 09 2019

Magma

[1] cat [39*38^(n-1): n in [1..20]]; // Vincenzo Librandi, Apr 28 2014

Maple

k:=39; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 09 2019

Mathematica

CoefficientList[Series[(1+x)/(1-38x), {x, 0, 20}], x] (* Vincenzo Librandi, Apr 28 2014 *)
With[{k = 39}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 09 2019 *)
Join[{1},NestList[38#&,39,20]] (* Harvey P. Dale, Aug 07 2025 *)

PARI

vector(26, n, k=39; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 09 2019

Sage

k=39; [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)*39^k. - Philippe Deléham, Dec 04 2009

a(0)=1; for n>0, a(n) = 39*38^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f.: (39*exp(38*x) - 1)/38. - G. C. Greubel, Oct 09 2019