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A170761
Expansion of g.f.: (1+x)/(1-41*x).
50
1, 42, 1722, 70602, 2894682, 118681962, 4865960442, 199504378122, 8179679503002, 335366859623082, 13750041244546362, 563751691026400842, 23113819332082434522, 947666592615379815402, 38854330297230572431482, 1593027542186453469690762
OFFSET
0,2
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
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 *)
PROG
(PARI) vector(26, n, k=42; if(n==1, 1, k*(k-1)^(n-2))) \\ 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
(Sage) k=42; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Oct 10 2019
(GAP) k:=42;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019
CROSSREFS
Cf. A003945.
Sequence in context: A170627 A170675 A170723 * A218744 A158727 A208779
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 04 2009
STATUS
approved