%I #31 Sep 08 2022 08:45:49

%S 1,21,420,8400,168000,3360000,67200000,1344000000,26880000000,

%T 537600000000,10752000000000,215040000000000,4300800000000000,

%U 86016000000000000,1720320000000000000,34406400000000000000,688128000000000000000,13762560000000000000000,275251200000000000000000

%N Expansion of g.f.: (1+x)/(1-20*x).

%H Kenny Lau, <a href="/A170740/b170740.txt">Table of n, a(n) for n = 0..768</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (20).

%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*21^k. - _Philippe Deléham_, Dec 04 2009

%F a(0) = 1; for n>0, a(n) = 21*20^(n-1). - _Vincenzo Librandi_, Dec 05 2009

%F E.g.f: (21*exp(20*x) - 1)/20. - _G. C. Greubel_, Sep 24 2019

%p k:=21; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Sep 24 2019

%t Join[{1}, 21*20^Range[0, 25]] (* _Vladimir Joseph Stephan Orlovsky_, Jul 13 2011 *)

%o (Python) for i in range(31):print(i,21*20**(i-1) if i>0 else 1) # _Kenny Lau_, Aug 01 2017

%o (PARI) vector(26, n, k=21; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Sep 24 2019

%o (Magma) k:=21; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Sep 24 2019

%o (Sage) k=21; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Sep 24 2019

%o (GAP) k:=21;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # _G. C. Greubel_, Sep 24 2019

%Y Cf. A003945, A097805.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Dec 04 2009