PROG
(MAGMAMagma) [1] cat [40*39^(n-1): n in [1..20]]; // Vincenzo Librandi, Dec 11 2012
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(MAGMAMagma) [1] cat [40*39^(n-1): n in [1..20]]; // Vincenzo Librandi, Dec 11 2012
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(MAGMA) k:=40; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 10 2019
GExpansion of g.f.: (1+x)/(1-39*x).
a(n) = Sum_[{k, =0<=k<=..n} A097805(n,k)*(-1)^(n-k)*40^k. [From _- _Philippe Deléham_, Dec 04 2009]
a(0) = 1; for n>0, a(n) = 40*39^(n-1). [From _- _Vincenzo Librandi_, Dec 05 2009]
E.g.f.: (40*exp(39*x) - 1)/39. - G. C. Greubel, Oct 10 2019
k:=40; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 10 2019
CoefficientList[Series[(1 + x)/(1 - 39*x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 10 2012 *)
With[{k = 40}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 10 2019 *)
(PARI) vector(26, n, k=40; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 10 2019
(MAGMA) k:=40; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 10 2019
(Sage) k=40; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Oct 10 2019
(GAP) k:=40;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019
Cf. A003945.
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<a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (39).
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a(n)= Sum_[k, 0<=k<=n} A097805(n,k)*(-1)^(n-k)*40^k. [From _Philippe DELEHAM_, Deléham_, Dec 04 2009]
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