A170766 Expansion of g.f.: (1+x)/(1-46*x).

1, 47, 2162, 99452, 4574792, 210440432, 9680259872, 445291954112, 20483429889152, 942237774900992, 43342937645445632, 1993775131690499072, 91713656057762957312, 4218828178657096036352, 194066096218226417672192, 8927040426038415212920832

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 (46).

Crossrefs

Cf. A003945.

Programs

GAP

k:=47;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019

Magma

k:=47; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 10 2019

Maple

k:=47; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 10 2019

Mathematica

CoefficientList[Series[(1+x)/(1-46*x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 09 2012 *)
With[{k = 47}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 10 2019 *)

PARI

vector(26, n, k=47; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 10 2019

Sage

k=47; [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)*47^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 47*46^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f.: (47*exp(46*x) - 1)/46. - G. C. Greubel, Oct 11 2019