A170761 Expansion of g.f.: (1+x)/(1-41*x).

1, 42, 1722, 70602, 2894682, 118681962, 4865960442, 199504378122, 8179679503002, 335366859623082, 13750041244546362, 563751691026400842, 23113819332082434522, 947666592615379815402, 38854330297230572431482, 1593027542186453469690762

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 (41).

Crossrefs

Cf. A003945.

Programs

GAP

k:=42;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019

Magma

k:=42; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 10 2019

Maple

k:=42; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 10 2019

Mathematica

CoefficientList[Series[(1+x)/(1-41*x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 10 2012 *)
With[{k = 42}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 10 2019 *)
Join[{1},NestList[41#&,42,20]] (* Harvey P. Dale, Feb 02 2022 *)

PARI

vector(26, n, k=42; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 10 2019

Sage

k=42; [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)*42^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 42*41^(n-1). - Vincenzo Librandi, Dec 05 2009

a(0)=1, a(1)=42, a(n) = 41*a(n-1). - Vincenzo Librandi, Dec 10 2012

E.g.f.: (42*exp(41*x) - 1)/41. - G. C. Greubel, Oct 10 2019