A170767 Expansion of g.f.: (1+x)/(1-47*x).

1, 48, 2256, 106032, 4983504, 234224688, 11008560336, 517402335792, 24317909782224, 1142941759764528, 53718262708932816, 2524758347319842352, 118663642324032590544, 5577191189229531755568, 262127985893787992511696, 12320015337008035648049712

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 (47).

Crossrefs

Cf. A003945.

Programs

GAP

k:=48;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019

Magma

k:=48; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 10 2019

Maple

k:=48; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 10 2019

Mathematica

CoefficientList[Series[(1+x)/(1-47*x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 09 2012 *)
With[{k = 48}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 10 2019 *)
Join[{1},NestList[47#&,48,20]] (* Harvey P. Dale, Nov 07 2021 *)

PARI

vector(26, n, k=48; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 10 2019

Sage

k=48; [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)*48^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 48*47^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f.: (48*exp(47*x) - 1)/47. - G. C. Greubel, Oct 11 2019