A170762 Expansion of g.f.: (1+x)/(1-42*x).

1, 43, 1806, 75852, 3185784, 133802928, 5619722976, 236028364992, 9913191329664, 416354035845888, 17486869505527296, 734448519232146432, 30846837807750150144, 1295567187925506306048, 54413821892871264854016, 2285380519500593123868672

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 (42).

Crossrefs

Cf. A003945.

Programs

GAP

k:=43;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019

Magma

k:=43; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 10 2019

Maple

k:=43; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 10 2019

Mathematica

CoefficientList[Series[(1+x)/(1-42x),{x,0,30}],x] (* or *) Join[{1}, NestList[42#&,43,30]] (* Harvey P. Dale, Mar 26 2012 *)
With[{k = 43}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 10 2019 *)

PARI

a(n)=if(n,43*42^(n-1),1) \\ Charles R Greathouse IV, Mar 22 2016

Sage

k=43; [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)*43^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 43*42^(n-1). - Vincenzo Librandi, Dec 05 2009

a(0)=1, a(1)=43, a(n)=42*a(n-1). - Harvey P. Dale, Mar 26 2012

E.g.f.: (43*exp(42*x) - 1)/42. - G. C. Greubel, Oct 10 2019