A170763 Expansion of g.f.: (1+x)/(1-43*x).

1, 44, 1892, 81356, 3498308, 150427244, 6468371492, 278139974156, 11960018888708, 514280812214444, 22114074925221092, 950905221784506956, 40888924536733799108, 1758223755079553361644, 75603621468420794550692, 3250955723142094165679756

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 (43).

Crossrefs

Cf. A003945.

Programs

GAP

k:=44;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019

Magma

[1] cat [44*43^(n-1): n in [1..20]]; // Vincenzo Librandi, Dec 11 2012

Maple

k:=44; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 10 2019

Mathematica

CoefficientList[Series[(1+x)/(1-43*x), {x, 0, 20}], x] (* Vincenzo Librandi, Dec 09 2012 *)
Join[{1},NestList[43#&,44,20]] (* Harvey P. Dale, Jan 15 2013 *)
With[{k = 44}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 10 2019 *)

PARI

a(n)=44*43^n\43 \\ Charles R Greathouse IV, Jul 01 2013

Sage

k=44; [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)*44^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 44*43^(n-1). - Vincenzo Librandi, Dec 05 2009

a(0)=1, a(1)=44, a(n) = 43*a(n-1). - Vincenzo Librandi, Dec 11 2012

E.g.f.: (44*exp(43*x) - 1)/43. - G. C. Greubel, Oct 10 2019