A170765 Expansion of g.f.: (1+x)/(1-45*x).

1, 46, 2070, 93150, 4191750, 188628750, 8488293750, 381973218750, 17188794843750, 773495767968750, 34807309558593750, 1566328930136718750, 70484801856152343750, 3171816083526855468750, 142731723758708496093750, 6422927569141882324218750

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 (45).

Crossrefs

Cf. A003945.

Programs

GAP

k:=46;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019

Magma

k:=46; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 10 2019

Maple

k:=46; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 10 2019

Mathematica

CoefficientList[Series[(1+x)/(1-45x),{x,0,15}],x]  (* Harvey P. Dale, Mar 26 2011 *)
With[{k = 46}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 10 2019 *)

PARI

a(n)=46*45^n\45 \\ Charles R Greathouse IV, Jun 16 2011

PARI

vector(26, n, k=46; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 10 2019

Sage

k=46; [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)*46^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 46*45^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f.: (46*exp(45*x) - 1)/45. - G. C. Greubel, Oct 10 2019