A170764 Expansion of g.f.: (1+x)/(1-44*x).

1, 45, 1980, 87120, 3833280, 168664320, 7421230080, 326534123520, 14367501434880, 632170063134720, 27815482777927680, 1223881242228817920, 53850774658067988480, 2369434084954991493120, 104255099738019625697280, 4587224388472863530680320

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 (44).

Crossrefs

Cf. A003945.

Programs

GAP

k:=45;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019

Magma

k:=45; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 10 2019

Maple

k:=45; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 10 2019

Mathematica

CoefficientList[Series[(1+x)/(1-44*x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 09 2012 *)
With[{k = 45}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 10 2019 *)
Join[{1},NestList[44#&,45,20]] (* Harvey P. Dale, Aug 22 2021 *)

PARI

vector(26, n, k=45; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 10 2019

Sage

k=45; [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)*45^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 45*44^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f.: (45*exp(44*x) - 1)/44. - G. C. Greubel, Oct 10 2019